7?^. /J 


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r) 


r) 


The  Inaccuracy  of  Movement 


WITH  SPECIAIi  REFERENCE  TO  CONSTANT  ERRORS 


BY 

H.  L.  HOLLINGWORTH,  Ph.D. 

TUTOR   IN   PSYCHOLOGY,    IN_BARNARD    COLLEGE,  COLUMBIA    UNIVERSITY 


ARCHIVES    OF   PSYCHOI.OGY 

BDITSD    BT 

B.  S.  WOODWOETH 


No.  13,  June,  1909 


NEW 

THE  SCIENOKPRESS 


Press  of 

The  new  Era  printing  Company 

Lancaster.  Pa. 


CONTENTS 

PAGE 

Intboduction  1 

CHAPTER    I 

Methods  of  Studying  Movements  3 

(a)    Extent    3 

(&)    Time    5 

(c)  Force    6 

(d)  Apparatus  of  the  Present  Study    7 

CHAPTER    II 

The  Illusion  Pboduced  by  Impact  10 

Experimental  Results  and  Interpretation 

CELA.PTER    III 

The  Indifference  Point  21 

Experimental  and  Theoretical 

CHAPTER    IV 

Relation  between  Extent  and  Duration  40 

(a)   Comparative  Accuracy    54 

( 6 )    Correlations    55 

(c)  Apparent  Direction  of  Errors    58 

(d)  Perception  of  Speed     61 

CHAPTER    V 
Memory  fob  Extent  and  Duration  63 

CHAPTER   VI 
Inflltince  of  the  Degree  of  Contraction   70 

CHAPTER    VII 

The  Criteria  of  the  Judgment  of  Extent  77 

Slmmary    81 


THE  INACCURACY  OF  MOVEMENT 

INTRODUCTORY 

The  student  of  the  psychology  of  movement  is,  to  say  the  least, 
not  hampered  by  the  novelty  of  his  subject.  Ever  since  the  days 
of  the  muscle  sense  controversy  investigator  after  investigator  has 
interested  himself  in  the  subject  of  movement  until  a  considerable 
body  of  motor  psychology,  in  turn  acclaimed  and  condemned,  has 
developed.  The  present  study  is  not  directly  concerned  with  the 
implications  of  movement,  nor  with  the  relation  of  movement  to 
mental  processes  with  which  an  analytic  psychology  is  largely  con- 
cerned. As  an  experimental  investigation  it  grew  out  of  a  number 
of  interesting  and  not  at  once  explicable  observations  of  constant 
errors  in  exercises  on  the  accuracy  of  the  perception  and  reproduc- 
tion of  arm  movements.  The  accuracy  of  movement  has  frequently 
been  the  subject  of  special  study,  from  different  points  of  view  and 
not  infrequently  with  varying  or  inconsistent  results.  As  has  often 
been  pointed  out,  this  inconsistency  is  partly  due  to  the  extreme 
complexity  of  the  sensations  aroused  by  the  movement  of  the  parts 
of  the  body  usually  employed — chiefly  the  upper  and  lower  limbs 
and  the  eyes.  Introspective  analysis  of  the  sensation  of  movement 
is  exceedingly  difficult.  Coming,  as  it  does,  from  a  great  number  of 
sources— the  muscles,  ligaments,  tendons,  articular  surfaces  and  skin 
—and  closely  associated  as  it  is  with  the  spatial  order  of  other  senses, 
particularly  that  of  vision,  it  seems  to  present  a  highly  complex 
fusion,  the  components  of  which  do  not  readily  yield  themselves  to 
the  efforts  of  introspective  discrimination. 

Further,  as  will  be  more  fully  developed  in  a  later  chapter,  the 
process  of  recognition  and  judgment  of  extent  seems  to  consist,  first, 
of  a  reference  of  the  movement  to  a  familiar  and  rather  loosely 
defined  group,  followed  by  its  approximate  recognition  as  this  or 
that  movement.  Many  of  the  constant  errors  and  illiLsions  of  move- 
ment may  be  found  to  depend  on  the  nature  of  this  process.  A  third 
source  of  discrepancy  in  comparative  results  is  shown  l)y  the  present 
experiments  to  lie  in  the  methods  of  control  and  record  used.  The 
present  experiments  seem  to  indicate  that  every  movement  as  judged 
tfnds  to  fi\]\  into  its  proper  place  in  the  objective  scale  of  magnitude 
as  determined  on  some  other  basis  than  the  intensity  or  extensity  of 
the  accompanying  sensations,  or  of  the  stimulus,  though  not  entirely 

1 


2  THE   INACCURACY    OF    MOVEMENT 

without  reference  to  these  factors.  Investigation  of  the  relations 
and  interdependencies  of  these  objective  characteristics  and  of  the 
influence  any  one  of  them  may  exert  on  the  judgment  of  any  other 
are  not  without  interest.  Not  a  few  such  researches  have  been  con- 
ducted, but  there  are  still  questions  that  have  not  been  satisfactorily 
answered,  sources  of  error  that  have  not  been  sufficiently  regarded, 
contradictory  results  that  have  not  yet  been  cleared  up,  and  interest- 
ing phenomena  which  seem  to  have  escaped  observation.  Theories 
as  to  the  more  fundamental  character  of  judgments  of  time  or  of 
extent  have  not  been  tested  in  any  direct  way,  illusions  of  over 
and  under  estimation  have  not  been  satisfactorily  accounted  for, 
statements  of  the  "law  of  forgetting"  for  spatial  and  temporal 
magnitudes  can  not  yet  be  generalized,  no  convenient  apparatus  for 
recording  simultaneously  the  extent,  speed,  duration  and  force  of 
movements  of  any  considerable  magnitude  has  yet  been  described. 
The  experiments  to  be  reported  in  the  following  chapters  were 
conducted  with  the  following  chief  things  in  mind: 

1.  The  desire  to  find  the  most  satisfactory  method  of  recording 
and  studying  voluntary  movements  of  the  limbs,  and  to  construct 
a  simple  apparatus  which  would  measure,  simultaneously,  all  the 
attributes  of  any  single  movement. 

2.  The  determination  of  the  relations  existing  between  the  percep- 
tions of  extent  and  of  duration  or  speed. 

3.  The  analysis  of  the  basis  of  the  positive  and  negative  constant 
errors  involved  in  the  phenomenon  of  the  shifting  or  periodic 
"indifference  point." 

4.  Investigation  of  the  extraordinary  positive  constant  errors  pro- 
duced by  the  force  of  impact. 

5.  The  testing  of  the  "duration"  hypothesis  in  the  constant  errors 
of  the  Loeb  illusion. 

6.  The  need  for  further  data  on  the  memorability  of  spatial  and 
temporal  perceptions. 

7.  The  unsatisfactoriness  of  most  expositions  of  the  basis  of  the 
judgment  of  equality  or  difference  in  the  case  of  space  magnitudes. 

The  experiments  were  performed  in  the  Psychological  Laboratory 
of  Columbia  University  during  the  years  1907-9,  under  the  directions 
of  Professors  Cattell  and  Woodworth.  The  writer  wishes  also  to 
express  his  obligation  to  Professor  T.  L.  Bolton,  of  the  University  of 
Nebraska,  under  whom  he  received  his  first  scientific  training  and  to 
whom  he  owes  his  first  interest  in  the  psychology  of  movement. 


CHAPTER   I 

]\Iethods  of  Studying  Movement 

In  this  chapter  will  be  considered  some  of  the  methods  employed 
by  various  other  investigators  in  this  field,  and  a  piece  of  apparatus 
especially  constructed  for  the  present  research  will  be  described— 
an  instrument  which  seems  in  many  ways  to  possess  advantages  over 
the  apparatus  heretofore  used.  In  the  succeeding  chapters  will  be 
reported  the  experimental  results  of  the  investigations  undertaken, 
with  a  discussion  of  their  significance  for  the  general  problem  of 
movement. 

(a)    Extent  of  Movement 

The  study  of  method,  always  important  to  the  success  of  an 
experimental  investigation,  has  special  significance  in  the  psychology 
of  movement.  The  divergent  results  of  different  investigators  in 
this  field  seem  more  frequently  to  indicate  the  peculiar  influence  of 
the  method  employed  than  to  display  the  character  of  the  perception 
of  movement  as  such.  The  first  and  most  comprehensive  study  of 
method  in  the  field  of  movement,  that  of  Cattell  and  Fullerton,^  was 
concerned  chiefly  with  the  investigation  of  the  reliability  and  influ- 
ence of  the  various  psycho-physical  methods,  the  mode  of  judgment 
and  of  record.  These  authors  conclude  that  "the  method  of  average 
error— in  which  the  observer  makes  one  stimulus  as  nearly  as  possible 
like  another— is  in  many  cases  the  most  convenient  of  methods, "=^ 
and  this  method  of  average  error  was  employed  throughout  the 
present  study.  But  the  chief  divergence  between  the  results  of 
different  authors  seems  to  have  been  caused  by  differences  in  the 
objective,  instrumental  methods  employed,  and  these  methods  require 
more  thorough  investigation  before  many  results  can  be  completely 
interpreted. 

The  controversy  over  the  question  of  rectilinear  and  curvilinear 
movement  seems  to  be  still  undecided.  Kiilpe^  and  Angier*  insist 
that  all  the  work  on  rectilinear  movement  is  worthless,  and  that  the 
whole  matter  must  be  worked  over,  using  movements  of  the  curvi- 
linear type— rotations  of  a  single  joint  in  a  single  plane,  while  Wood- 
worth^  has  clearly  pointed  out  that  "the  force  of  this  objection  is 

'"On  the  Perceplifjii  oi  Small    Ditrcnmccs,"   1892. 
'Ibid.,  1.51. 
•"Outlines,"  .341. 
*Zeit.  f.  I'sychol.,  39,  4.30,  1905. 
""Le  Mouvenient,"  PariK,  Doin,  l!t0.3,  8(». 

3 


4  THE   ^ACCURACY    OF   MOVEMENT 

more  apparent  than  real."  The  matter  need  not  concern  us  here, 
since  we  are  not  interested  in  the  statement  of  the  absolute  quanti- 
tative accuracy  of  either  the  perception  or  the  reproduction  of  move- 
ments, nor  in  a  determination  of  individual  differences,  nor  in  any 
attempt  to  give  topographical  location  to  the  source  of  the  sensations 
of  movement.  In  only  one  case,  that  of  the  experiments  on  the 
degree  of  contraction,  would  the  type  of  movement  used  suggest  any 
possible  source  of  error  for  the  problem  set.  But  since  other  experi- 
menters have  shown  the  Loeb  illusion  to  occur  with  curvilinear  as 
well  as  with  rectilinear  movement,  even  here  the  type  of  movement 
is  irrelevant  to  the  topic  under  consideration. 

The  methods  of  active  and  passive  movement  have  also  frequently 
led  to  somewhat  different  results,  but  it  has  been  generally  recognized 
that  the  two  situations  are  qualitatively  different,  and  this  disparity 
of  method  has  seldom  led  to  erroneous  interpretation.  In  fact  this 
has  happened  only  in  cases  in  which  the  block  method,  next  to  be 
discussed,  was  employed  in  the  active  movements  and  the  peculiar 
error  characteristic  of  this  method  allowed  to  pass  unexamined. 

The  traditional  method  of  controlling  the  extent  of  a  movement 
to  be  judged  is  by  impact  of  the  moving  member  or  the  carriage 
against  an  upright.  The  possibility  of  error  in  the  use  of  this 
method  has  already  been  suggested  incidentally  by  Titchener®  and 
by  Segsworth.'^  The  latter  regrets  that  no  other  method  is  possible 
unless  shadows,  photography  or  some  other  such  optical  apparatus 
be  employed.  The  objections  made  to  the  method  are  that  groups 
of  other  sensations,  consisting  of  contact,  pressure  and  resistance, 
are  brought  about,  and  "complicate  the  judging  of  the  pure  motion 
sensations." 

The  present  study  will  show*  that  this  method  introduces  a  large 
positive  constant  error,  which  is  a  function,  in  part,  of  the  force 
of  impact  against  the  block,  and  the  magnitude  of  which  causes  a 
corresponding  increase  in  the  variable  error.  The  only  other  prin- 
cipal method  which  seems  to  have  been  previously  used  is  the  "free" 
method,  by  which  the  subject  makes  a  movement  which  is  self-con- 
trolled as  to  extent  and  time.  Then  having  made  this  free  and 
predetermined  movement,  another  movement  is  made  which  is  to  be 
equal  to  the  first.  The  faultiness  of  this  method  is  apparent.  What 
the  subject  tends  to  do  is  to  endeavor  to  make  two  movements  accord- 
ing to  a  mental  standard,  which  may  even  be  so  standardized  as  to 
be  expressed  in  inches  or  millimeters.     It  is  not,  in  this  case,  a  matter 

""Exper.  Psychol.,"  Vol.  II.,  Pt.  2,  260. 

''  Amer.  Jour,  of  Psychol.,  6,  .369,  1894. 

'  Chapter  II. 


METHODS    OF    STUDYING    MOVEMENT  5 

of  the  reproduction  of  a  previous  movement.  Indeed  the  perception 
of  extent  hardly  enters  except  as  the  subject  is  required,  after  having 
made  the  two  movements,  to  indicate  their  relative  magnitude — to 
guess  at  his  probable  error.  In  this  case  it  is  at  all  events  hard  to 
secure  ■\vell-distributed  and  uniform  records. 

From  still  another  point  of  view  there  are  two  methods,  both  of 
which  have  been  used  by  different  investigators.  These  may  be 
called  the  continuous  and  the  successive  methods.  With  the  con- 
tinuous method,  the  starting  point  of  the  second  movement  coincides 
with  the  terminal  point  of  the  first  one.  The  two  movements  are 
thus  not  only  made  with  a  different  degree  of.  contraction  of  the 
muscle,  but  in  some  cases  different  or  additional  muscles  are  brought 
into  play.  This  would  of  course  be  no  objection  from  the  point  of 
view  of  one  who  adheres  to  the  joint  sense  theory.  But  as  a  matter 
of  fact  a  constant  error  is  here  introduced,  the  nature  of  which  will 
be  pointed  out  in  the  next  chapter.  The  other  method  also  presents 
difficulties.  Kramer  and  Moskiewicz  claim  that  in  reproducing  from 
an  identical  starting  point,  a  tendency  to  grope  for  the  same  terminal 
position  results,  and  the  feeling  of  movement  reduces  to  a  feeling  of 
position.  This  tendency  is  clearly  present  in  the  case  of  some  sub- 
jects. But  it  seems  that  one  method  or  the  other  must  be  used,  for 
no  other  practical  alternative  has  yet  been  suggested. 

The  apparatus  later  to  be  described  is  designed  to  eliminate  many 
of  the  errors  arising  from  this  diversity  of  methods. 

(&)    Time  of  Movement 

Aside  from  reaction  experiments,  fewer  studies  have  been  made 
of  the  time  of  movement  than  of  its  extent.  This  has  been  chiefly 
on  account  of  the  difificulty  of  conveniently  recording  and  controlling 
the  time  of  movements  of  any. considerable  magnitude.  Intrinsically 
the  subject  is  of  great  interest.  By  means  of  the  instrument  devised 
for  the  present  study  the  duration  of  a  movement,  its  speed  at  any 
point  in  its  course,  as  well  as  its  extent,  are  graphically  recorded. 
^Moreover  the  movement  may  be  as  much  as  a  meter  in  length,  al- 
tliough  extremely  small  movements  are  recorded  with  equal  accuracy. 

It  may  be  well  to  point  out  the  methods  heretofore  employed  for 
the  registration  of  this  type  of  movement.  The  first  investigators 
were  Camerer'*  anrl  Viorordt.^"  The  sn])ject  was  required  to  rest  his 
fingers  on  the  top  of  a  brass  rod,  whifh  was  hinged  at  one  end.  The 
other  end  bore  a  writing  point  wliicli  recorded  the  movement  on  a 
horizontal  rotating  drum.      This  di-iiiii  was  turned  by  hand  and  the 

'"  VfTHiiphf  iil).  (1.  zcitl.  \'(Tlaiif  d.  \\ill('iislK'\v('f,'ung,"  Diss.,  Tiibin{,'c>ii,  18GG. 

""' Zcitsinn,"  Tfihin^cn,  1808,  .3.3. 


6  THE   INACCURACY    OF    MOVEMENT 

time  of  the  movement  calculated  on  the  basis  of  a  time  line  afforded 
by  an  induction  apparatus.  With  this  method  the  extent  of  the  move- 
ments studied  was  limited  to  a  very  few  millimeters.  Binet  and 
Courtier"  worked  with  rather  limited  writing  movements,  using  an 
Edison  electric  pen.  The  needle  of  this  pen,  actuated  by  an  eccentric 
at  the  rate  of  about  11,000  times  per  minute,  pricked  holes  in  a  roll 
of  paper.  Interesting  results  were  suggested,  but  on  account  of 
mechanical  difficulties  nothing  very  definite  could  be  stated.  The 
rate  of  11,000  punctures  per  minute  was  too  rapid  to  allow  any 
accurate  calculation.  And  if  the  rate  was  lowered  the  needle  caught 
in  the  perforations,  tearing  the  paper  and  interfering  with  its  own 
regularity.  Leuba,^^  in  an  unpublished  study,  describes  an  instru- 
ment to  be  carried  by  the  index  finger,  the  slightest  movement  of 
which  makes  a  contact  which  is  broken  by  lifting  the  finger  into  the 
air.  The  time  is  recorded  on  a  kymograph  drum.  No  experimental 
results  have  yet  been  reported,  but  since  the  mechanism  involves  a 
reaction  time  at  the  termination  of  the  movement  it  seems  probable 
that  the  natural  course  and  character  of  the  movement  would  be 
disturbed  by  this  additional  feature.^^  Jaensch^*  w^orked  with  a  hol- 
low pen  holder  containing  a  spring  connected  with  a  Marey  tambour. 
The  pen  was  pressed  down  by  the  subject  at  the  beginning  and  end 
of  each  movement,  thus  recording  the  time  of  the  movement  on  the 
drum  by  jerks  in  the  line  but  necessitating  a  reaction  time  and  a 
distracting  performance  at  each  end  of  the  movement.  Cattell  and 
Fullerton^^  have  described  the  instrument  at  present  used  in  the 
Columbia  laboratory  in  connection  with  a  Hipp  chronoscope.  The 
beginning  of  a  movement  closes  a  circuit  which  is  broken  at  the 
completion,  thus  registering  the  time  from  the  beginning  of  the 
movement  to  the  moment  at  which  the  circuit  is  broken.  The  chief 
difficulty  in  the  use  of  this  instrument  and  of  the  Witmer  modifica- 
tion of  it  employed  by  Gault^^  will  be  pointed  out  in  Chapter  V. 

(c)    Force  of  Movement 

In  most  of  the  work  done  on  this  subject— so  far  as  I  have  been 
able  to  learn,  in  all  except  the  work  of  Cattell  and  Fullerton^^— the 

^^  Revue  Philosophiquc,  35,  664,  1893. 

"Fifteenth  Report,  Am.  Psychol.  Ass.,  1906,  218. 

"  Leiiba  has  since  exhibited,  before  the  American  Psychological  Association, 
December  20,  1908,  a  device  for  recording  independently  the  extent  and  duration 
of  forearm  movements. 

"  Zeit.  f.  Psychol,  41,  257,  1907. 

"Op.  cit.,  103. 

"  Am.  Jour,  of  Psychol.,  16,  357,  1905. 

"Op.  cit.,  66. 


Plate  I 


METHODS   OF   STUDYING    MOVEMENT  7 

force  of  movement  has  been  a  direct  function  of  the  extent.  This 
is  especially  true  of  the  vast  amount  of  work  that  has  been  done  on 
the  ergograph.  Under  these  conditions  it  has  been  impossible  to  say- 
how  far  the  judgment  was  concerned  with  the  pure  force  or  energy 
of  the  movement  and  how  far  it  had  to  do  with  the  perception  of 
extent  as  a  secondary  criterion.  Consequently  in  constructing  the 
instrument  about  to  be  described  provision  was  made  for  the  study 
of  the  force  of  movement  under  conditions  which  allow  the  percep- 
tion of  force  to  be  made  independently  of  the  perception  of  extent. 

(d)  The  Apparatus  and  IMethod  of  the  Present  Study 
As  a  foundation  for  the  instrument  the  Cattell-Fullerton  appa- 
ratus for  the  study  of  extent  of  movement  was  used.  This  has 
already  been  described  by  these  authors  as  consisting  of  "a  brass 
plate  one  meter  long,  graduated  to  millimeters  and  grooved  for  the 
wheels  of  a  small  brass  carriage  (see  Plate  2).  Along  the  scale  is  a 
wire,  carrying  an  indicator  (i)  which  is  moved  by  a  bar  (6)  attached 
to  the  carriage.  Between  the  front  and  back  wheels  of  the  carriage, 
and  parallel  with  the  track,  is  a  ring  (t)  into  which  is  inserted  the 
finger  used  in  moving  the  carriage.  .  .  .  The  carriage  may  be  moved 
alone  or  used  to  raise  any  weight  (w)  attached  to  the  cord."^^  For 
the  purposes  of  the  present  experiments  a  number  of  modifications 
have  been  made.  In  order  to  more  completely  eliminate  the  noise 
made  by  the  moving  carriage,  wood-fiber  wheels  have  been  substi- 
tuted in  place  of  the  original  metal  ones.  When  a  little  machinist's 
oil  is  placed  in  the  grooves  of  the  track,  the  car  now  runs  smoothly 
and  noiselessly.  In  place  of  the  original  uprights  for  controlling 
the  extent  of  the  standard  movements,  a  sound  hammer  (h,  Plate  1) 
is  arranged  in  circuit  with  the  car  and  the  indicator  (i)  which  slides 
on  the  wire.  The  contact  made  by  the  bar  running  out  from  the 
carriage  and  the  brass  indicator  completes  an  independent  electric 
circuit  which  runs  through  the  hammer  magnet.  The  stroke  of  the 
hammer  serves  as  a  signal  for  the  stopping  of  the  movement.  The 
constant  error  of  impact,  later  to  be  pointed  out,  is  thus  avoided, 
and  whatever  reaction  time  is  involved  is  included  in  the  original 
time  and  extent  of  the  movement. 

For  recording  the  duration  of  movements  the  following  device  is 
employed.  To  the  top  of  the  carriage  is  attached  a  signal  magnet 
(m)  which  controls  the  vibrations  of  an  enlarged  Pfeil  time  marker 
(s).  The  magnet  circuit  is  infcrrnptod  i)y  means  of  a  reed  oscillator 
(v),  vibrating  at  the  rate  of  ton  times  per  scccmd.  This  gives  ten 
main  vibrations  of  the  time-marker  per  second  (c').  But  in  order 
"  Op.  cit.,  35. 


g  THE   INACCURACY    OF    MOVEMENT 

to  make  interpolation  easier  and  more  accurate  a  thin  piece  of 
rubber  is  glued  on  the  face  of  the  magnet  core  (m).  This  produces 
a  rebound  (c-)  of  the  spring  of  the  time-marker  in  the  middle  of 
each  main  vibration.  The  tenths-of-a-second  curve,  produced,  when 
the  carriage  is  moved,  by  the  simple  vibrations,  is  thus  transformed 
into  a  twentieth-of-a-second  curve,  each  tenth  being  represented  by 
a  large  deflection  of  the  tracing  point,  and  each  intervening  twen- 
tieth by  a  somewhat  smaller  deflection.  By  interpolating  within 
these  twentieths,  the  time  of  a  movement  can  be  determined  to  within 
one  hundredth  of  a  second. 

The  writing  point  (p)  of  the  time  marker  consists  of  a  thin  brass 
extension  terminating  in  a  piece  of  flexible  gelatine.  The  record  is 
made  on  a  smoked  paper  (x)  stretched  on  a  horizontal  frame  which 
slides  underneath  the  track  from  the  side  of  the  apparatus  on  which 
the  operator  stands.  This  frame  is  made  of  well  seasoned  wood,  and 
is  prevented  from  warping  by  means  of  a  thin  steel  lining  running 
along  both  sides.  Each  side  and  end  of  the  frame  consists  of  four 
layers— first  a  layer  of  wood,  then  in  turn  a  layer  of  cork,  another 
layer  of  wood,  and  finally  the  steel  lining.  Over  the  frame  is  tacked 
a  foundation  of  cardboard,  which  serves  to  support  the  glazed  paper 
while  it  is  being  attached  and  smoked.  The  paper  is  stretched  out 
over  the  frame  and  fixed  in  place  by  strips  of  cardboard.  Thumb 
tacks  through  the  cardboard  and  into  the  cork  layer  of  the  frame  are 
easily  inserted  or  removed.  After  the  paper  is  thus  fixed  in  place 
on  the  frame  the  smoking  is  easily  accomplished  by  moving  the  in- 
verted frame  above  the  camphor  flame. 

For  studying  the  perception  and  reproduction  of  the  force  of 
movement,  the  carriage  is  made  to  pull  against  a  pair  of  coiled 
springs  (r,  r'),  placed  below  the  box  which  supports  the  track  at  the 
proper  elevation  for  making  convenient  movements  of  the  carriage. 
These  springs  are  so  adjustable  that  the  force  may  be  varied  inde- 
pendently of  the  extent,  but  may  be  correlated  with  it  empirically, 
and  in  a  relation  unknown  to  the  subject.  Thus  the  first  or  standard 
movement  may  be  made  against  one  spring  at  a  given  degree  of  ten- 
sion, while  the  second  movement  may  be  made  against  a  different 
spring,  against  the  same  spring,  or  against  both.  A  pulley  attach- 
ment (a)  provides  for  the  use  of  weights  instead  of  springs  if  such 
an  experiment  is  desired. 

"We  may  thus  secure,  simultaneously,  a  graphic  record  of  the 
duration,  speed,  extent,  and  force  of  a  given  movement,  along  with 
an  indication  of  any  irregularities  that  may  occur  in  its  performance. 
The  method  of  procedure  is  simple  enough.  By  closing  a  convenient 
key  (5,  Plate  2)  on  the  table  before  him  the  operator  sets  the  time 


Plate  II 


METHODS    OF   STUDYING    MOVEMENT  9 

marker  in  vibration.  At  a  signal  from  the  operator  or  at  an  inde- 
pendently chosen  moment,  the  subject  begins  his  movement.  At  the 
sound  of  the  hammer  signal  he  stops  the  movement,  and  the  hammer 
circuit  is  broken  by  the  operator  by  throwing  another  switch  («') 
near  at  hand.  Before  the  carriage  is  returned  to  the  starting  point 
the  magnet  circuit  is  also  broken.  During  the  movement  the  writing 
point  has  traced  the  compound  time-curve  on  the  paper.  As  the 
carriage  is  returned,  the  writing  point  traces  a  straight  line  which 
divides  the  previously  inscribed  record  in  such  a  way  that  the  tenths 
of  a  second  may  be  read  off  on  one  side  of  the  line.  For  the  rebounds 
of  the  Pfeil  spring,  when  the  current  is  off,  come  beyond  the  straight 
line,  registering  tenths  of  seconds.  But  the  rebounds  when  the  circuit 
is  closed  are  of  smaller  amplitude,  and  come  only  to  the  straight  line 
without  crossing  it.  These  vibrations  are  ignored  when  counting  in 
tenths,  but  when  counting  in  twentieths,  both  the  vibrations  (c') 
reaching  beyond  the  line  and  those  extending  only  to  it  (c')  are 
regarded. 


CHAPTER    II 


.Off 


The  Illusion  Produced  by  Impact 

In  a  series  of  experiments  performed  previous  to  those  repoi 
in  this  series,  the  traditional  method  of  controlling  the  extent  . 
movement  to  be  judged  by  blocking  it  by  means  of  an  upright 
employed.     It  was  soon  observed  that  the  impact  of  the  m^ 
against  the  upright  produced  a  large  constant  error  in  the 
tion  of  the  movement.     This  constant  error  was  aVa^' 
was  frequently  so  great  as  to  astonish  the  opera^ 
to  suspect  that  the  observer  was  not  paying  the  le^  jn  to  the 

experiment.  But  careful  observations  of  ha:  ^  dozen  subjects 
showed  that  the  illusion  was  present  in  all  cases  and  exp'^^-'ments 
were  made  to  test  the  direction,  amount  and  persistence  of  the  error. 

In  Table  I.,  for  Observer  Lk.,  typical  results  are  shown  for  free 
and  blocked  movements.  In  the  case  of  the  free  movements  the 
standard  Avas  in  each  case  a  spontaneous  movement  the  extent  of 
which  was  determined  by  the  subject.  A  standard  movement  was 
made  and  then  this  standard  reproduced  as  nearly  as  possible.  The 
standard  movements  were  deliberately  varied  between  75  and  350  mm. 
The  error  in  per  cent,  was  then  calculated  for  each  movement,  and 
movements  between  75  mm.  and  125  mm.  grouped  under  column 
100  mm.,  movements  between  125  mm.  and  175  mm.  under  column 
150  mm.,  etc.  Thus,  in  Table  I.,  the  first  column  under  each  heading 
(100,  150,  etc.)  shows  the  average  per  cent,  error  tor  movements 
ranging  around  the  magnitude  indicated  by  the  heading  as  central 
tendency,  and  not  deviating  from  this  magnitude  by  more  than 

TABLE    I 

Free  and  Blocked  Standaeds 

Observer  Lk. 


100 

150 

200 

250 

300 



a 

mm. 

^ 

mm. 

?« 

mm. 

^ 

mm. 

a 

mm. 

A.E. 

23 

23 

14 

21 

14 

28 

10 

25 

9 

-.    o  • 

2 

C.E. 

+  18 

+  10 

+  10 

+  15 

+11 

+  22 

+  7 

+18 

—  4 



V.E. 

12 

12 

13 

20 

10 

20 

12 

30 

8 

-i 

A.E. 

155 

155 

110 

165 

60 

120 

30 

lb 

15 

15 

t 

C.E. 

+155 

+155 

+110 

+165 

+60 

+120 

+  30 

+75 

+15 

+44 

eq 

V.E. 

28 

28 

27 

41 

15 

SO 

13 

33 

9 

27 

10 


THE    ILLUSIOy    PRODUCED    BY    IMPACT  H 

25  mm.     The  second  column  gives  the  error  in  mm.,  found  by  multi- 
plying the  central  tendency  by  the  average  error  in  per  cent.     In  the 
3corded  in  the  lower  part  of  Table  I.  the  subject  was  simply 
>d  to  move  along  the  track  until  his  movement  was  blocked, 
"^he  upright  was  then  removed  and  the  movement  was  continued,  in 
an  endeavor  to  make  the  two  extents  equal.     The  table  gives  the 
■>»''flss  average  error,  the  constant  error  and  the  variable  error,  in 
'io  ^m-  and  in  per  cents  of  the  standard,  fifty  trials  being  made 
•aci^  magnitude  under  each  t>i)e  of  movement.     In  both  cases  the 
'Oions"  method  was  used— the  terminal  point  of  the  first  move- 
'  "iTipr  as  the  starting  point  of  the  second.     Any  other  method 
^'.twfe.-e  with  the  illusion.     Thus  if  the  car  had  been 
•  •  ''ItiaX  position  and  the  second  movement  made  over 
the  sam  .    <Bf  track,  the  illusion  produced  by  the  impact  would 

tend  to  be  parts.  \!  ..corrected  by  the  more  careful  and  precalculated 
move^^^'^nt  back  to  the  starting  point. 

The  upper  half  of  Table  I.  gives  the  records  for  the  free  move- 
ments. The  constant  error  for  observer  Lk.  is  seen  in  this  case  to 
be  slightly  positive  except  for  the  largest  movement,  where  it  becomes 
negative.  It  never  becomes  greater  than  22  mm.  and  the  variable 
error,  except  in  one  case,  is  less  than  25  mm.  The  lower  half  of  the 
table  gives  the  results  for  the  blocked  movements,  in  which  the  sub- 
ject started  to  move  along  the  track,  knowing  that  at  some  point  he 
would  be  blocked  by  the  upright,  but  being  in  no  case  aware  of  the 
point  at  which  the  block  was  to  occur.  In  these  experiments  the 
constant  error  is  always  positive,  and  becomes  from  two  to  eight 
times  as  large  as  in  the  case  of  the  free  movements.  Indeed,  in  the 
case  of  the  100  mm.  and  150  mm.  movements,  the  positive  constant 
error  is  larger  than  the  original  standard,  meaning  that  the  repro- 
duced movement  was  more  than  twice  as  long  as  it  ought  to  have 
been.  As  a  consequence  of  this  large  constant  error  we  come  to  deal 
with  quantities  of  much  greater  magnitude  than  with  the  free  stan- 
dards, and  the  variable  error  becomes  correspondingly  larger,  be- 
coming now  as  large  as  28  per  cent,  whereas  before  it  never  exceeded 
15  per  cent.  It  is  obvious  that  under  such  conditions  we  are  not 
studying  the  normal  accuracy  of  movement,  but  are  measuring  the 
;.jeffect  of  impact  on  the  perception  of  extent. 

jr      That  this  is  true  is  shown  conclusively  in  Table  II.     Tlie  purpose 
'r>i  these  experiments,  on  another  observer,  was  to  discover  in  what 
iegree  the  illusion  is  a  function  of  thf  force  of  impact.     At  tlu^  bid- 
■"ding  of  the  operator  the  observer  started  wjih  the  iiilciilion  of  moving 
one  foot,  two  feet  or  three  feet  as  tlic  case  might  be.      By  tliis  pro- 
cedure the  speed  of  the  movement  was  varied  quite  uniformly,  since 


12 


TEE   INACCURACY    OF    MOVEMENT 


TABLE    II 

Influence  of  Force  of  Impact 

Observer  El. 


Blocked  at 


Intent  to  move. 


Speed. 

A.E.  of  speed. 
C.E.  per  cent. 
V.E.  per  cent. 


10  cm. 


1ft. 


2  ft. 


68  1  100 

3  2 

+138  I  +174 

SO  i  4^ 


3  ft. 


110 
6 

+171 
41 


20  cm. 


1ft. 


32 
9 

+100 
S4 


2  ft. 


120 

7 
+158 


3  ft. 


138 

5 

+166 


30  cm. 


2  ft. 


103 

9 

+90 


3  ft. 


155 

8 
+132 

28 


large  movements  tend  to  be  made  more  rapidly  than  smaller  ones, 
and  the  variations  of  speed  would  of  course  make  a  corresponding 
variation  of  the  force  of  impact  against  the  upright.  In  some  cases 
the  movement  was  blocked  at  10  cm.,  at  20  cm.  or  at  30  cm.,  at  the 
option  of  the  operator.  As  a  matter  of  fact,  a  chance  order  was 
adopted  throughout,  care  being  taken  that  in  the  long  run  the  same 
number  of  each  kind  was  given.  This  number,  as  in  the  previous 
experiment,  was  50.  But  the  movement  was  not  blocked  in  all  cases. 
In  50  cases  for  each  magnitude  the  subject  was  allowed  to  actually 
make  the  movement  of  1  foot,  2  feet  or  3  feet,  which  was  his  original 
intention.  Then  after  the  regular  interval  he  went  on  to  reproduce 
this  movement.     The  records  for  these  trials  are  given  in  Table  III. 

TABLE    III 

Showing  Averages  in  mm.  of  Free  Movements   (1)   Intended  to  Equal 

1  ft.,  2  ft.  and  3  ft.,  and  averages  of  reproductions   (2)   of 

THESE  Free  Standards,  with  Errors  in  Percentage 

Observer  El. 


To  move 

1  ft. 

2  ft. 

3  ft. 

Av.  1  (mm.). 

217 

371 

485 

Av.  2  (mm. ). 

259 

385 

454 

A.  E.  per  cent. 

19 

4 

6 

C.E.  per  cent. 

+21 

+6 

—6 

V.  E   per  cent. 

13 

12 

11 

After  having  made  these  experiments,  the  actual  speed  at  the 
various  points  of  blocking,  under  the  different  conditions,  was  com- 
puted on  the  basis  of  ten  movements  of  each  of  the  standard  magni- 
tudes. The  speed,  in  each  case,  is  given  in  terms  of  mm.  passed  over 
during  the  twentieth  of  a  second  preceding  and  the  twentieth  of  a 
second  after  the  particular  point  of  blocking  in  question. 

Examination  of  the  tables  discloses  several  points  of  interest. 
Thus,  in  Table  II.,  reading  across  on  the  level  of  any  one  block  point, 
as  at  20  cm.  under  1  foot,  2  feet  and  3  feet,  the  positive  constant 
error  is  seen  to  increase  directly  with  the  force  of  impact  as  indicated 


THE   ILLUSION    PRODUCED    BY    IMPACT  13 

in  terms  of  speed  or  velocity,  +  100  at  speed  32,  +  158  at  speed  120 
and  +  166  at  speed  138.  Whether  this  increase  is  proportional  or 
not  can  not  easily  be  made  out,  because,  since  the  continuous  method 
was  used  in  the  reproductions,  the  second  movements  were  in  each 
case  subject  to  the  negative  error  pointed  out  in  the  chapter  on  the 
influence  of  the  degree  of  contraction  (Chapter  VII.).  This  of 
course  means  that  the  positive  error  is  in  all  cases  really  greater  than 
it  appears  from  the  record,  since,  in  addition  to  producing  a  positive 
error,  it  has  counteracted  the  normal  negative  error. 

The  speed  curve  of  ordinary  movements  of  a  given  extent  has 
been  found  to  be  rather  uniform  and  typical.^  The  movement  begins 
gradually  and  increases  in  velocity  until  about  the  middle  of  the 
extent,  slowing  down  again  as  it  approaches  the  end.  "In  all  eases 
the  middle  point  of  the  extent  coincides  almost  exactly  with  the  mid- 
point of  the  duration. ' '  ^Moreover,  the  maximum  speed  attained  in 
executing  a  normal  long  movement  is  higher  than  that  of  an  equally 
normal  movement,  made  under  the  same  circumstances  but  of  less 
extent.  The  average  speeds  of  the  movements  in  the  present  experi- 
ments were  found  to  be  for  the  1-,  2-  and  3-foot  standards,  70,  103 
and  113  mm.  respectively,  per  tenth  of  a  second.  Thus,  when  the 
observer  intended  to  make  a  movement  of  2  feet,  the  speed  at  10  cm. 
averaged  100  mm.  per  .1  sec,  with  a  M.V.  of  only  2  mm.  At 
20  cm.  the  movement  had  attained  a  speed  of  120  mm.  with  a  M.V. 
of  7  mm.,  while  at  30  cm.  the  speed  was  decreasing  as  the  movement 
approached  its  goal,  averaging,  at  this  point  103  mm.,  with  a  M.V. 
of  9  mm.  The  20-cm.  point  would  thus  seem  to  be  approximately 
the  mid-point  of  the  movement,  although  the  subject  felt  himself  to 
be  making  a  2-foot  (about  60  cm.)  movement.  If  we  refer  to  Table 
III.  we  find  this  to  be  really  the  case,  since  the  average  attempt  to 
make  a  2-foot  movement  averaged  a  little  over  37  cm.,  and  half  of 
this  extent  does  not  take  us  far  short  of  the  20-cm.  point.  Similarly 
the  one-foot  movement  is  slowing  down  at  20  cm.,  while  the  3-foot 
movement  is  still  increasing  in  speed  at  30  cm. 

Reading  across  under  the  corresponding  columns  of  the  three 
sections  of  Table  II.,  the  constant  error  seems  to  be  rather  inde- 
pendent of  the  speed  at  the  different  block  points.  Thus  in  the  2-foot 
column,  when  blocked  at  10  cm.,  the  C.E.  is  +174;  blocked  at 
20  cm.,  with  higher  speed  (120),  the  C.E.  is  only  -f-  158,  while  at 
the  30-cm.  block,  although  the  speed  is  still  103,  the  C.E.  is  but 
+  90.  Similarly,  in  the  3-foot  column  the  blocks  at  10,  20  and 
30  cm.,  with  increasing  speeds  of  110,  138,  155,  the  C.E.  decreases 

'  liiiK't  and  CVjnrticr.  op.  ml.,  (]('>4. 


14  THE   INACCURACY    OF    MOVEMENT 

through  +  171,  +  166,  +  132.  Although  the  errors  are  always 
positive,  and  strikingly  so,  in  these  vertical  columns  the  greater  error 
may  occur  when  the  speed  is  least.  This  seems  to  indicate  that  the 
same  or  a  greater  impact  may  mean,  nevertheless,  a  smaller  illusion, 
according  as  it  stands  near  to  or  far  from  the  end  of  the  movement, 
but  that  it  always  means  an  illusion.  The  greater  the  amount  of  the 
movement  already  accomplished,  the  smaller  the  illusion.  The  indi- 
cation seems  to  be  that  a  movement  checked  by  the  block  method  half 
way  towards  completion  is  not  the  same  thing  mentally  as  a  move- 
ment half  as  large  as  the  original  one,  but  at  the  same  time  a  unit, 
beginning  and  ending  under  control.  The  first  movement  contains 
a  variety'  of  elements  of  distraction,  chief  of  which  are  the  original 
intention  and  the  effect  of  impact. 

The  magnitude  of  the  illusion  seems  thus  to  bear  no  exact  mathe- 
matical relation  to  the  force  of  impact,  but  to  be  highly  complicated 
by  other  factors  when  such  are  present.  But,  other  things  being 
equal,  the  dependence  seems  to  be  direct  and  proportional.  It  is  at 
least  sufficiently  clear  that  some  method  other  than  that  of  the  block 
should  be  used  in  the  study  of  movements.  Consequently,  in  the 
experiments  to  follow,  the  signal  method,  already  described  ( Chapter 
I.),  is  to  be  used.  This  method  eliminates  the  elements  of  distrac- 
tion and  illusion,  while  at  the  same  time  enabling  easy  variation  and 
control  of  the  magnitude  of  the  standard  extent.  All  movements 
studied  are  then  unitary  movements,  and  can  be  properly  compared 
with  any  other  free  movement. 

There  seems  to  be  no  possibility  of  making  a  general  statement 
that  will  express  in  quantitative  terms  the  effect  of  practise  on  the 
magnitude  of  an  illusion  of  perception.  Thus  in  recent  contributions 
we  find  these  two  statements:  "Practise  affects  the  variable  error 
but  not  the  constant  error";  "Practise  decreases  the  magnitude  of 
an  illusion."  Now  a  constant  error  is  an  illusion.  Illusion 
takes  place  when  an  experience  is  taken  to  be  what  it  is  not. 
In  these  constant  errors  of  movement  we  have  just  such  a  situa- 
tion. An  extent  is  estimated  to  be  what  it  is  not,  and  this  seems 
to  signify  that  some  internal  event,  process  or  effect  is  also  mis- 
judged. It  may  be  of  interest  to  observe  the  effect  of  practise  on 
the  illusion  of  impact.  Table  IV.  shows  the  result  of  seven  days' 
practise,  by  another  observer,  without  knowledge  of  results,  and  of 
seven  days'  later  practise  with  knowledge.  The  procedure  here  was 
the  same  as  in  the  former  experiments,  except  that  after  the  seventh 
day  the  observer  was  told  immediately  after  each  reproduction 
whether  his  second  movement  was  "too  short,"  "right"  or  "too 
long."      (This  was  only  in  the  case  of  the  blocked  movements.)      No 


TEE    ILLUSIOX    PRODUCED    BY    IMPACT 


15 


statement  of  the  amount  of  the  error  was  made.  Each  record  in  the 
table  is  the  average  of  five  trials  for  the  particular  magnitude  on  the 
day  in  question.  Through  the  first  week  the  constant  error  is  seen 
to  have  increased  quite  uniformly  from  day  to  day,  practise,  in  the 
sense  of  repetition,  instead  of  decreasing  the  illusion  having  just  the 
reverse  effect.  The  V.E.,  however,  remained,  on  the  whole,  rather 
constant. 

TABLE    IV 
Effect  of  Practise  ox  the  Impact  Iixfsiox 

Observer  V. 


Average  of  Five 

Trials  for  each 

Magnitude. 

100 

mm. 

150 

mm. 

200 

mm. 

250 

mm. 

300 

mm. 

1907 

Fr. 

Blk. 

Fr. 

Blk. 

Fr. 

Blk. 

Fr. 

Blk. 

Fr. 

Blk. 

Dec. 

r  c.E. 

V.E. 

13 

11 

89 
20 

29 
10 

63 

U 

25 

8 

75 

23 

19 

9 

31 

10 

40 
7 

27 
7 

26 

6 

C.E. 
V.E. 

24 
9 

171 
SO 

41 

10 

111 

^5 

15 
i5 

51 

10 
5 

35 
5 

7 

22 
9 

27 

C.E. 
V.E. 

14 

17 

137 

40 

20 

8 

94 

13 

21 
6 

69 
3 

12 
10 

37 

16 

—13 
6 

33 

5 

28 

c 

i4  ^ 

C.E. 
V.E. 

37 
14 

150 
16 

37 

7 

83 

11 

56 

30 

7 

47 

9 
7 

28 
6 

29 

c 

1 

C.E. 
V.E. 

C.E. 
V.E. 

30 
IS 

59 
19 

154 

27 

99 

25 

28 

2 

47 
7 

92 

85 
15 

27 

29 
8 

48 
i5 

53 

5 

43 

8 

19 

43 

11 

43 

26 
i5 

20 
6 

41 
29 

30 
31 

C.E. 
.  V.E. 

43 

18 

123 

44 

50 

5 

97 
5(? 

43 
(5 

63 

28 

47 
5 

15 

7 

34 
10 

Jan. 
1 

\   C.E. 
V.E. 

37 
13 

63 

27 

44 

8 

60 
29 

32 

17 

31 

12 

30 
8 

2 

13 

5 

7 

2 

C.E. 
V.E. 

19 
6' 

45 

32 

20 
15 

45 

17 

2i 

27 
i(9 

5 
5 

13 

4 
16 

—  9 

"5 

3 

C.E. 
V.E. 

10 
9 

74 

23 

34 

6 

43 

26 
6 

7 
5 

15 
6 

5 

6 

5 
5 

—  5 

4 

o  , 

c 

C.E. 

V.E. 

26 

12 

54 

29 

13 
1 

31 

8 

13 

6 

1 
5 

13 
5 

—11 
5 

16 

—  6 

7 

5 

1 

C.E. 
V.E. 

16 
8 

70 
£6 

11 
6 

19 

6 
5 

12 
4 

12 

—  1 

16 

6 
3 

—  4 

12 

6 

C.E. 
V.E. 

16 
10 

63 
IS 

24 
18 

21 

11 

19 
8 

18 
15 

23 
9 

8 
5 

6 
5 

—  5 
5 

7 

C.E. 
,  V.E.   1 

24 
9 

47 
18 

35 
6 

25 

21 

5 

6! 
ii  1 

12 

6' 

—  8 
11 

4 

8 

—10 
9 

8 

During  the  second  week  the  effect  of  knowledge  was  simply  to 
.shorten  all  reproduction.s.  For  the  shorter  movements  the  C.E.  thus 
became  smaller  but  remained  positive  throughout,  while  the  previous 
positive  error  for  tho  lonfr  movomonts  })f'camo  decidedly  negative. 


16 


THE   IXACCURACY    OF    MOVEMENT 


Apparently  the  effect  of  practise,  as  well  as  of  knowledge,  is  not  to 
decrease  the  illusion,  but  to  provoke  a  deliberate  shortening  of  the 
reproductions  against  the  observer's  own  judgment.      The  C.E.  for 

TABLE    V 

Effect  of  Peactise  on  the  Impact  Illusion 

Observer  Chr. 


Average  of  Five 

100 

mm. 

150 

mm. 

200 

mm. 

250 

mm. 

300 

mm. 

1907. 

Trials  for  Each 
Magnitude 

Fr. 

Blk. 

Fr. 

Blk. 

Fr. 

Blk. 

Fr. 

Blk. 

Fr. 

Blk. 

Dec. 

r  c^E. 

V.E. 

31 
6 

224 
84 

12 

4 

141 

44 

24 

13 

157 
14 

9 
11 

75 
9 

—  1 

7 

69 
77 

1 

C.E. 
V.E. 

13 

6 

214 

£0 

25 

i5 

90 
18 

28 
9 

113 

^9 

—   5 

52 
SI 

2 

(5 

43 
20 

2 

C.E. 
V.E. 

7 
U 

99 

18 

—  4 

52 

10 
25 

25 
4 

—  3 

6 

22 

7:5 

—  1 
7 

9 

5 

3 

C.E. 
V.E. 

—  3 
13 

39 

15 

0 
.?7 

54 
50 

0 

12 

40 
i5 

0 

7 

17 
70 

10 
76 

2 

8 

4 

C.E. 
V.E. 

2 

10 

88 
4S 

9 
8 

24 
17 

7 
75 

35 

54 

—  4 

18 
19 

—  7 
7 

13 

5 

5 

C.E. 
V.E. 

1 

13 

52 

40 

1 

u 

37 

5 

—  1 

10 

3 

5 

—14 
4 

4 

2 

6 

—  3 
77 

6 

6 

0) 

C.E. 
V.E. 

7 
13 

64 
40 

2 
11 

46 
16 

—10 

5 

31 

7 

—  5 

if 

25 
77 

3 

7 

2 
74 

9 

g- 

C.E. 
V.E. 

—12 
6 

18 

33 

-12 

7 

33 
i(5 

—  2 

7 

10 
13 

—  5 

5 

9 
6 

—  1 

7 

1 
.9 

10 

i 

C.E. 
V.E. 

—11 

11 

45 

27 

—  9 
9 

31 

-  1 

7 

10 

—  1 
4 

5 
(5 

—  9 

2 

0 
9 

11 

C.E. 
V.E. 

—25 
10 

27 
12 

1 

15 

29 
11 

2 
6 

26 

-| 

2 

7 

-11 

5 

0 

7 

12 

C.E. 
V.E. 

—23 
4 

21 
16 

-  6 

12 

8 
5 

—  3 

7 

8 

-  1 

6 

—  6 

5 

—  4 
5 

—14 
6 

13 

C.E. 
V.E. 

6 

27 

SI 

1 
6 

18 
19 

4 
■4 

9 
5 

—  4 
5 

4 
5 

3 

5 

3 
5 

14 

C.E. 
V.E. 

—  1 
4 

16 
19 

20 

44 
i5 

10 

19 
IS 

0 
4 

7 
5 

—15 
3 

1 
5 

16 

C.E. 
V.E. 

—  4 
8 

26 
11 

—  2 
6 

28 

2 

5 

19 

2 
70 

—  4 

7 

5 

5 

—  5 
70 

17 

C.E. 
,  V.E. 

—  5 
6 

1 
5 

9 

9 

7 

3 
5 

5 

—  2 
77 

4 

1 
4 

1 
5 

18 

the  long  movements,  which  was  less  proportionately  than  that  for  the 
shorter  ones,  was  shortened  sufficiently  to  be  transformed  into  a 
negative  error.  Here  again  the  V.E.  remains  little  changed  through- 
out. Table  V.,  for  still  another  observer,  for  two  weeks,  with  cor- 
rective knowledge  from  the  beginning,  and  five  daily  trials  for  each 


THE    ILLUSIOX    PliODUCED    BY    IMPACT  17 

record,  for  both  free  and  blocked  movements,  shows  much  the  same 
effect.  The  variable  errors  remain  practically  unchanged,  the  posi- 
tive constant  errors  for  the  blocked  movements  become  quickly  re- 
duced, while  the  constant  errors  for  the  free  movements,  beginning  as 
positive,  soon  become  almost  entirely  negative.  The  real  illusion 
still  persists,  and  the  deliberate  attempt  to  correct  it  miscarries  in 
producing  an  opposite  error  for  the  free  movements.  Another  experi- 
ment, on  a  fifth  observer  for  fourteen  days  shows  the  same  persist- 
ence of  the  illusion  and  the  same  disastrous  effect  of  the  deliberate 
corrective  attempts. 

The  eff'ect  of  these  corrective  attempts  on  the  reproduction  of 
free  movements  is  not  unlike  the  suggestive  results  of  Solomons'^ 
experiment  on  two-point  discrimination,  and  seems  to  throw  some 
light  on  the  nature  and  basis  of  the  judgment  of  extent.  Solomons' 
experiment  demonstrated  the  susceptibility  to  suggestion  of  the 
"judgment  of  twoness"  and  its  lack  of  connection  with  judgments 
of  area,  position,  etc.  These  facts  seemed  to  indicate  that  the  judg- 
ment is  at  bottom  but  a  matter  of  simple  association.  "AVe  learn 
that  a  certain  kind  of  sensation  means  two  points,  just  as  we  learn 
that  certain  marks  mean  the  letter  H,  that  another  group  of  sensa- 
tions means  "book,"  etc.  In  the  experiment  referred  to  the  two- 
point  and  one-point  touches  were  purposely  made  to  differ  in  two 
other  features— mode  of  application  and  locality— the  two-point 
touch  being  made  by  a  sharp  blow,  in  one  area,  the  one-point  being 
applied  more  by  pressure  and  always  in  another  area.  After  a 
period  of  practise  the  conditions  were  reversed— "the  double  points 
now  pressed  down  and  in  the  place  where  the  single  point  was  for- 
merly applied,  while  the  single  touch  is  made  with  a  blow  and  in  the 
place  where  at  the  start  the  double  touch  was  made. ' '  Under  these 
circumstances  the  judgment  was  reversed— two  is  called  one  and  one 
two.  ' '  The  peculiarities  of  the  sensation  due  to  the  method  of  appli- 
cation and  the  locality,  have  completely  superseded  those  due  to  the 
number  of  points,  as  a  basis  for  the  judgment."  His  conclusion  is 
that  any  cutaneous  sensation  may  give  rise  to  a  perception  of  two 
contacts  if  the  past  experience  of  the  individual  has  established 
the  proper  associations,  and  that  there  seem  to  be  reasons  for  sup- 
posing that  the  same  holds  for  other  cutaneous  judgments— position, 
area,  etc. 

Our  present  experiment  affords  indications  of  a  similar  asso- 
ciative and  empirical  basis  for  the  judgment  of  extent  of  movement. 
In  the  beginning  of  the  experiment  the  movements  of  the  subject 
were  made  on  some  already  present  basis  of  comparison  — a  certain 

*  Psychol.  Rev.,  4,  240,  1897. 


18  THE    INACCURACY    OF    MOVEMENT 

movement  in  one  region  of  the  arm's  total  possible  swing  was  felt 
as  equal  to  a  certain  other  movement.  Introspectively  the  basis 
satisfied  the  demands  of  the  experiment.  But  objectively  the  impact 
disturbance  induced  striking  discrepancy  in  the  judgments  of 
equality.  So  long  as  this  discrepancy  entailed  no  serious  conse- 
quence the  old  system  of  criteria  persisted  and  the  error  went  unper- 
ceived.  But  as  soon  as  the  subject  became  aware  of  the  large  con- 
stant error  in  his  reproductions,  the  desire  for  objective  equality  led 
to  a  transformation  of  the  basis  of  judgment.  The  old  signs  of 
magnitude  could  no  longer  be  relied  on.  At  the  end  of  the  second 
week  this  new  basis  had  become  fairly  well  established  and  the  accu- 
racy of  reproduction  of  the  impact  movements  approximates  the 
original  accuracy  of  the  free  movements.  The  effect  of  this  newly 
established  basis  on  the  judgment  of  free  movements  is  significant. 
The  correction  which  is  appropriate  in  the  case  of  impact  movements 
is  not  restricted  to  these  only,  but  is  carried  over  into  the  other  situ- 
ation. This  is  most  clearly  shown  in  Table  V.,  but  appears  also  in 
the  case  of  the  larger  movements  in  Table  IV.  Movements  in  the 
first  part  of  the  arm's  swing,  the  standard  extents,  are  the  same. 
But  the  scale  of  criteria  of  extent  in  the  further  portion  of  the  arm's 
swing  has  been  shifted  downward,  an  objectively  shorter  movement 
having  been  learned  to  be  the  equivalent  of  the  standard  extent. 
When  these  standards  become  free  movements  the  newly  acquired 
scale  continues  to  be  utilized.  Since  no  correction  was  made  in  the 
case  of  these  free  movements,  we  may  suppose  that  this  scale  would 
in  its  turn  persist  until  objective  necessities,  awareness  of  error,  or, 
in  case  the  impact  movements  were  dropped  out,  the  gradual  re- 
assertion  of  the  older  and  more  firmly  established  system,  led  to 
modification  in  one  direction  or  another.  Such  results,  along  with 
those  of  Solomons,  not  only  tend  to  lead  to  an  empirical  theory  of 
space  perception,  but  persuade  one  to  go  the  empiricist  one  better. 
Judgments  of  extent  of  movement  do  not  seem  to  be  dependent  on 
an  anatomically  conditioned  topographical  relation  between  points 
on  sensitive  membranes  (joint  linings)  and  points  in  external  space, 
or  on  any  fixed  serial  order  of  stimulations  of  skin,  tendon  or  muscle. 
As  was  the  case  with  the  judgment  of  twoness — the  judgment  of 
equality  of  extent  seems  to  be  at  bottom  a  matter  of  simple  associa- 
tion— those  movements  are  judged  to  be  equal  which  have  been 
learned  to  he  equal — any  sensation  quality  which  adequately  iden- 
tifies or  differentiates  a  given  movement  being  sufficient  to  serve  as 
basis  for  the  judgment  of  the  equality  or  difference  of  this  movement 
and  any  other  movement  with  a  similarly  adequate  and  equally  well 


TEE   ILLUSION    PRODUCED   BY   IMPACT  19 

learned  sensation  quality.^     The  significance  of  this  associative  basis 
of  equivalence  will  be  further  discussed  in  Chapter  VII. 

The  cause  of  the  impact  illusion  is  not  very  clear.  Three  con- 
tributory factors  seem  to  be  present:  (1)  the  original  intention,  (2) 
the  irradiation  of  the  stimulus,  (3)  the  shock  of  impact,  as  a  sensa- 
tion in  its  own  right. 

1.  The  Original  Intention.— This  first  factor  is  probably  an  im- 
portant one.  The  subject  sets  out  to  make  a  movement  of,  say,  two 
feet,  and  is  blocked  at  10  cm.  Now  the  process  of  preparing  for, 
innervating  and  beginning  a  movement  of  two  feet  is  not  just  like 
any  other  experience.  It  requires  a  particular  attitude,  a  particular 
more  or  less  widely  spread  adjustment,  and  a  particular  operation  of 
visual  and  motor  imagery.  It  seems  quite  likely,  then,  that  in  the 
reproduction,  the  observer  tends  not  so  much  to  move  over  the  dis- 
tance he  was  allowed  to  go  before,  but  to  repeat  the  original  perform- 
ance—to take  the  same  general  attitude,  and  make  the  same  innerva- 
tion. And,  since  there  is  no  block  in  the  way,  the  reproduction  tends 
to  approximate  the  original  intention  of  the  first  movement,  and  the 
resulting  error  is  always  positive.  This  explanation  might  be  suffi- 
cient if  the  illusion  occurred  only  in  such  cases.  But  in  the  case  of 
the  four  subjects  in  which  there  was  no  such  explicit  intention  we 
find  the  same  error  manifested.  In  all  four  of  these  cases  the  ob- 
server was  simply  told  to  move  his  finger  along  the  track,  knowing 
that  at  some  point  his  movement  would  be  blocked.  The  shock  of 
impact  might  be  expected  at  any  moment,  and  the  only  intention 
present  was  to  keep  on  moving  until  the  shock  came.  And  this  mild 
intention  is  certainly  inadequate  to  account  for  a  positive  constant 
error  of  155  per  cent,  of  the  standard. 

2.  Irradiation.— The  irradiation  of  the  stimulus  of  the  shock  of 
impact  may  have  caused  the  articular  surface  to  be  stimulated  farther 
on,  at  points  where  it  would  have  been  stimulated  had  the  movement 
actually  been  of  greater  magnitude.  Strict  adherents  of  the  joint 
sense  as  the  basi>s  of  judgments  of  extent  of  movement  might  find 
here  a  possible  explanation  of  the  illusion.  Or  the  irradiation  need 
not  be  conceived  as  restricted  to  the  articular  surfaces.  Tensions, 
strains,  compressions  and  various  local  signs  of  a  qualitative  or 
intensive  kind  are  doubtless  provoked  in  adjacent  and  outlying 
regions  of  the  muscles,  tendons  and  skin  as  well,  and  these,  being 
ordinarily  as.sociated  with  greater  movements,  may  assist  in  pro- 
ducing the  present  illusion. 

3.  The  Sensation  Itself.— The  illusion  may  come  under  the  gen- 

•  Messenger  (Psych.  Rev.,  Monograph  22,  1003)  seems  to  find  a  similar 
basis  for  the  perception  or  recognition  of  numl)cr. 


20  THE   IXACCURACY    OF    MOVEMENT 

eral  head  of  the  phenomena  of  fusion,  the  shock  of  impact  fusing 
^Yith  the  perception  that  is  uppermost  in  consciousness,  increasing  its 
sensory  elements  and  thus  the  apparent  magnitude  of  its  object.  The 
influence  of  a  secondary  stimulus  in  producing  an  apparent  increase 
in  a  primary  stimulus  is  a  common  experience.  In  the  case  of 
vision  this  influence  has  been  found  to  be  proportional  to  the  intensity 
of  the  secondary  stimulus.*  We  foimd  this  to  be  in  general  the  case 
in  this  illusion.  The  effect  of  such  an  influence  is  always  ' '  the  tend- 
ency to  fusion  of  two  or  more  sensations  which  are  simultaneously 
experienced."  The  extent  of  a  movement  and  the  force  of  a  blow 
may  seem  at  first  thought  to  be  not  only  incommensurable  but  in- 
capable of  summation,  but  both  are  equally  perceptions  of  magnitude, 
and  Woodworth  has  shown  that  "there  is  a  certain  amount  of  cor- 
relation between  the  extent  of  the  preliminary  movement  and  the 
force  of  the  blow.  "^ 

Whatever  explanation  we  prefer,  the  significance  of  the  illusion 
in  the  study  of  the  accuracy  of  movement  is  clear.  Thus  in  Angler's 
recent  study*'  he  finds  that  passive  movements  are  more  accurately 
perceived  than  are  active  movements.  Earlier  investigators  found 
the  reverse  to  be  true.  Now  from  the  description  of  the  method  used 
in  his  experiments,  it  appears  that  Angler's  results,  in  the  case  of 
active  movements,  were  subject  to  this  error  produced  by  impact.  It 
is  then  quite  conceivable  that  the  error  of  the  active  movements 
should  be  unfairly  increased  until  it  exceeded  that  of  the  passive 
movements,  although  under  similar  or  equally  favorable  circum- 
stances just  the  reverse  might  have  been  obtained.  IMiinsterberg'' 
used  the  same  method  for  controlling  the  standard  in  his  experiments 
in  sense  memory,  and  all  but  one  of  his  subjects  showed  extremely 
large  positive  constant  errore.  In  the  case  of  the  smallest  magnitudes, 
5  cm.,  this  positive  error  w^as  nearly  always  100  per  cent,  or  slightly 
less,  decreasing  rather  uniformly  with  increase  in  the  standard  mag- 
nitude. The  statement  of  the  amount  of  error  under  such  circmn- 
stances  can  not  be  said  to  express  the  fidelity  of  the  memory  for  sen- 
sations of  movement.  Even  if  the  C.E.  is  eliminated,  the  V.E.  will 
be  too  great  by  virtue  of  the  greater  magnitudes  involved.  Besides, 
one  is,  in  such  an  experiment,  measuring  not  only  the  memory  for 
extent  as  such,  but  at  the  same  time  the  rate  of  decrease  in  vividness 
of  the  illusion. 

*  H.  J.  Pearce,  "  Law  of  Attraction  in  Illusion,"  Psychol.  Rev.,  11,  43,  1904. 
""Vol.  Control  of  Force  of  Movement,"  Psychol.  Rev.,  8,  350-9,  1901. 
» Zeit.  f.  Psychol,  39,  430,  1905. 
'  Beitrage,  4,  69-88. 


CHAPTER   III 

The  Indifference  Point 

By  the  "indifference  point"  is  meant  the  point  in  a  scale  of 
magnitudes  at  which  there  is  no  constant  error  of  estimation.  "When 
estimates  or  reproductions  of  such  magnitudes  are  attempted  the 
general  rule  is  that  the  smaller  are  judged  or  reproduced  too  large 
while  the  greater  are  underestimated.  At  some  mean  magnitude 
onl}'  the  variable  error  is  found,  and  judgments  at  this  point  are 
consequently  more  precise.  The  region  about  this  mean  magnitude 
has  been  called  the  "indifference"  point,  more  properly,  the  region 
of  indifference.  The  phenomenon  of  the  "indifference  point"  seems 
to  have  been  first  observed  in  experiments  on  the  time-sense.  Vier- 
ordt,^  writing  on  the  basis  of  Camerer's  experiments,  found  that 
"there  is  an  unexceptionable  law  that  small  intervals  are  overesti- 
mated and  reproduced  so  on  the  kymograph,  whereas  longer  times 
are  inevitably  shortened."  Vierordt  also  states  that  the  "indiffer- 
ence point"  is  not  absolutely  fixed,  but  varies  with  different  indi- 
viduals and  at  different  times  in  the  same  individual.  "It  depends 
especially  on  the  conditions  of  the  experiment,  as  well  as  on  the  sense 
investigated."  But  the  "conditions  of  the  experiment"  were  not 
specified,  and  it  will  be  seen  later  that  Vierordt  himself  was  misled 
by  disregarding  them. 

From  the  time  of  Vierordt  the  long  array  of  investigators  of  the 
time-sense  set  themselves  the  problem  of  the  constant  error,  and 
sought  to  find  an  indifference  point  which  would  be  the  true  one. 
Horing,-  Kollert,^  Estel,*  Glass,^  Nichols,*'  Schumann'^  and  Stevens,^ 
in  turn,  found  regions  of  indifference,  but  at  varying  points  in  the 
scale,  e.  g.,  Horing  at  about  .5  sec,  Kollert  at  about  .8  sec,  Glass 
at  2  to  5  sec,  Nichols  at  about  1  sec  and  Stevens  .7  sec  on  one 
occasion  and  3  sec.  on  another.  Periodically  recurring  "indifferent 
points"  were  asserted  and  denied,  and  numerous  attempts  made  to 
relate  the  unit  of  periodicity  to  various  bodily  processes,  such  as 

'"Zeitsinn,"  18G8,  p.  17. 
^Dissertation,  Tubingen,  1864. 
^Phil.  Stud.,  1,  78,  1882. 
*Ihid.,  2,  37,  1884. 
'Ibid.,  4,  423,  1887. 
•  Amer.  Jour,  of  Psychol.,  3,  453,  1890. 
^  Zeit.  f.  Psychol,  u.  Hinn.,  2,  294,  1891. 
« Am.  Jour,  of  Psychol,  13,  1,  1902. 

21 


22  THE   INACCURACY    OF    MOVEMENT 

breathing,  pulse,  swing  of  leg,  etc.  These  points  will  be  more  fully 
referred  to  after  the  present  experiment  is  described.  But  the 
futility  of  attempting  to  relate  the  I.P.  (as  we  shall  hereafter  desig- 
nate the  "indifference  point")  to  the  temporal  periods  of  organic 
processes  should  have  become  apparent  as  soon  as  it  was  found  to 
be  a  characteristic  of  all  our  judgments  of  serial  magnitudes,  both 
temporal  and  non-temporal.  Vierordt  had  suggested  that ' '  a  similar 
relation  is  to  be  found  in  our  spatial  judgments,"  but  since  the 
temporal  relations  of  motor  processes  play  so  large  a  part  in  our 
spatial  judgments,  it  may  well  have  been  supposed  that  the  constant 
error  in  the  case  of  space  magnitudes  is  "simply  the  consequence 
of  the  rapidity  of  movement — hence  a  phenomenon  of  temporal 
estimation  as  well.  "'^ 

But  the  I.P.  is  also  found  in  judgments  of  weight,  force  and 
brightness,  as  well  as  in  those  of  time  and  extent.  In  all  these 
fields,  again,  there  is  little  agreement  among  investigators,  though 
there  is  usually  a  tendency  to  speak  of  the  I.P.  as  though  it  were 
in  each  case  some  absolute  and  fixed  region.  In  the  estimation  of 
force  the  I.P.  is  variously  placed  at  from  200  to  1,600  grams. 
Cattell  and  Fullerton,  using  seven  observers,  with  a  series  ranging 
from  200  to  1,600  grams,  found  the  I.P.  to  be  in  all  cases  between 
400  and  800  grams.  Wreschner,  studying  the  perception  of  lifted 
weights,  found  an  I.P.  at  1,200  grams  and  generalizes  by  saying  that 
high  intensities  weaken  in  the  memory  while  low  ones  are  strength- 
ened, a  certain  moderate  intensity  remaining  unchanged,  in  both 
one-hand  and  two-hand  experiments.  Leuba,^"  experimenting  with 
memory  for  brightness  intensities,  finds  a  striking  difference  between 
the  ratios  at  the  lower  and  upper  ends  of  the  scale.  "There  seems 
to  be  a  natural  tendency  to  shift  the  sensation  held  in  memory 
towards  the  middle  of  the  scale  of  intensities."  In  other  words, 
low  lights  are  overestimated  while  high  ones  are  under-rated.  The 
recent  work  of  Lewis^^  gives  some  evidence  in  confirmation  of 
Leuba's  results. 

All  experimenters  on  the  extent  of  movement  seem  to  have 
found  regions  of  indifference,  flanked  above  and  below  by  negative 
and  positive  constant  errors.  And  although  these  I.P. 's  all  differ 
among  themselves,  it  has  still  been  the  custom  to  refer  to  the  indif- 
ference point  as  thought  it  were  an  absolute  something.  Thus 
Kramer  and  ]\Ioskiewicz  and  Jaensch  surmise  that  there  is  such  a 
thing  as  a  "most  favorable"  extent,  as  well  as  a  "most  favorable" 

»  Kiilpe,  "  Outlines,"  343. 

^°Amer.  Jour,  of  Psychol,  5,  370,  1892. 

1'  Johns  Hopkins  Studies,  No.  2.    Psych.  Rev.,  Mon.  Supp.,  No.  40,  55,  1909. 


THE   ISr DIFFERENCE   POINT  23 

time.  Schneider/-  working  with  distances  ranging  from  70  to  100 
mm.  finds  an  I.P.  at  90  mm.,  Delabarre^^*  locates  it  at  about  300^00 
mm.,  Falk^*  at  70-80  mm.,  and  Miinsterberg  at  100-200  mm.,i5  while 
Cattell  and  Fullertoni«  find  it  to  be  100  for  one  observer,  300  for 
another  and  600  for  a  third.  It  was  the  disparity  of  these  results 
in  the  extent  of  movement  which  suggested  the  present  experiment, 
for  while  differences  of  a  fraction  of  a  second  in  the  case  of  experi- 
ments on  time  may  be  considered  quite  possibly  due  to  individual, 
mechanical  and  experimental  conditions,  the  difference  between  70 
mm.  and  600  mm.  within  the  possible  range  of  horizontal  arm  move- 
ments calls  for  some  other  explanation. 

That  no  such  explanation  has  been  suggested  is  shown  by  the 
fact  that  in  the  most  recent  and  thorough  review  of  the  subject  of 
movement  these  disagreements  are  merely  stated,^'  without  being 
brought  under  any  general  law.  There  is  still  the  tendency  to  treat 
the  I.P.  as  a  fixed  magnitude  of  yet  undetermined  location,  without 
specific  regard  to  the  series  in  which  it  occurs,  although  Vierordt 
long  ago  remarked  that  the  actual  magnitude  of  the  I.P.  depended 
on  the  "category"  in  which  it  was  placed. 

The  present  attempt  to  demonstrate  the  general  law  for  the  ap- 
pearance of  the  I.P.  phenomenon  grew  out  of  experiments  on  the 
accuracy  of  reproduction  of  active  and  passive  movements.  In 
this  experiment  small  magnitudes  were  employed,  the  particular 
lengths  ranging  from  43  to  100  mm.  In  nearly  every  case,  both 
for  the  active  and  the  passive  movements,  a  constant  error  was  found, 
which  was  positive  for  the  small  magnitudes  and  negative  for  the 
relatively  large.  The  region  of  indifference  was  found  between  60 
and  75  mm.,  falling  at  about  the  middle  of  the  series.  These  figures, 
taken  alone,  tend  to  confirm  Falk's  statement.  But  another  series 
of  experiments  with  the  Cattell-Fullerton  apparatus,  using  a  range 
of  100-300  mm.,  resulted,  in  several  subjects,  in  a  quite  uniform 
I.P.  at  about  200  mm.,  thus  agreeing  with  Miinsterberg,  who  used 
a  similar  apparatus  with  about  the  same  magnitudes.  Nevertheless, 
the  subjects  of  Cattell  and  Fullerton,  attempting  to  reproduce  from 
memory  the  extents  used  in  their  experiments,  100,  300,  500  and 
700  mm.,  showed  an  I.P.  between  300  and  500.  The  inference  that 
the  difference  here  found  was  purely  a  function  of  the  series  seems 


12  il 


"  La  Memoire  des  Mouvements  Actifs,"  Diss.  Juriew,  1894. 

'  Bewegunsemfindungen,"  89. 
"  "  Raumschiitzung  mit  Hiilfe  von  Arnibewegungen,"  Diss.  Dorpat,  1890. 
'^Beitrage,  2,  159. 
^Op.  cit.,  51. 
'  Woodworth,  "  Le  Mouvement,"  Chapt.  VI. 


24  TEE   INACCURACY    OF    MOVEMENT 

obvioiis.  Yet  in  the  field  of  the  time  sense  as  well  as  in  the  field 
of  movement,  there  had  been,  since  the  days  of  Vierordt  and  Cam- 
erer,  attempts  to  find  the  real  ' '  indifference  point, ' '  each  investigator 
using  such  series  limits  as  seemed  to  suit  his  convenience,  apparently 
with  no  suspicion  that  the  I. P.  might  be  purely  a  function  of  the 
upper  and  lower  limits  of  the  scale  of  magnitudes  in  the  particular 
experiment. 

In  order  to  test  this  suspicion  in  the  field  of  movement,  the 
following  experiment  was  made.  A  standard  series  of  magnitudes 
was  chosen,  ranging  from  10  mm.  to  250  mm.,  and  this  series  was 
divided  into  three  sections.  A,  B  and  C.  The  magnitudes  of  section 
A  ranged  from  10  mm.  (increasing  by  increments  of  10  mm.)  to 
70  mm.  Those  of  section  C,  from  70  to  250  mm.,  with  increments 
of  30  mm.,  and  those  of  section  B,  from  30  to  150  mm.,  with  incre- 
ments of  20  mm.,  thus  overlapping  the  inner  ends  of  sections  A 
and  C.  There  were  thus  seven  standard  magnitudes  in  each  section, 
and  the  three  sections.  A,  B  and  C  represented  respectively  the 
lower,  middle  and  upper  regions  of  the  total  scale  {S)  originally 
selected.  The  standards  were  made  by  cutting  a  narrow  slit  of 
the  desired  length  in  one  strip  of  cardboard  and  pasting  this  strip 
upon  another  such  strip  as  foundation.  This  formed  a  furrow  which 
served  as  adequate  guide  for  the  stylus  of  a  Delabarre  pendulum 
planchette,  or  for  the  blunt  point  of  a  heavy  carbon  pencil  which 
might  be  held  between  the  thumb  and  fore-finger  while  the  forearm 
rested  on  the  planchette  board.  The  furrow  was  carefully  rubbed 
with  graphite,  thus  affording  a  smooth  and  noiseless  track. 

Experiments  were  now  designed  with  the  following  purposes 
in  mind.  (1)  To  see  whether  a  periodic  I.P.  could  be  found  within 
the  total  series  (S),  by  working  with  its  special  sections,  finding  an 
I.P.  in  A,  one  in  B  and  another  in  C.  (2)  To  see,  for  instance, 
whether  the  same  absolute  magnitude  might  be,  under  one  circum- 
stance an  LP.,  under  another  circumstance  affected  with  a  positive 
constant  error,  or  again,  with  a  negative  constant  error.  (3)  To 
ascertain  whether  the  gradual  extension  of  the  series  limits  would 
be  accompanied  by  a  corresponding  change  in  the  position  of  the 
I.P.  (4)  To  find  whether  any  magnitude  in  the  series  evinced  any 
constant  error  when  estimated  out  of  relation  to  a  series  or  section. 
(5)  To  learn  whether  or  not  the  C.E.'s  occur,  even  in  serial  experi- 
ments, when  the  separate  trials  are  distributed  over  a  considerable 
period  of  time. 

Procedure. — A  Delabarre  pendulum  planchette,  with  a  14-foot 
radius,  was  suspended  over  the  outer  edge  of  a  writing  table  of 


TEE    INDIFFERENCE    POINT 


25 


comfortable  height.  The  observer  sat  with  his  left  forearm  on  the 
board,  with  the  carbon  pencil  held  between  thumb  and  forefinger. 
The  position  of  the  hand  was  made  constant  by  inserting  the  end  of 
the  little  finger  in  the  pen  shaft  of  the  board.  The  observer  wore 
the  blind  mask  throughout  or  worked  with  closed  eyes.  The  board 
swung  an  inch  and  a  half  clear  of  the  table,  on  which  lay  several 
large  sheets  of  smooth  white  paper.  One  of  the  standard  strips  was 
now  placed  underneath  the  board  and  the  point  of  the  carbon  pencil 
inserted  at  the  beginning  of  the  guide  slit.  The  cards  of  varying 
magnitudes  were  always  placed  so  that  the  center  of  the  board,  when 
the  pendulum  was  at  rest,  was  directly  over  the  halfway  mark  of 
the  slit.  The  observer  could  now  trace  the  path  with  a  minimum 
of  interference  and  adjustment,  and  with  practically  a  horizontal 
swing  of  the  forearm,  the  actual  movement  being  thus  rectilinear, 
a  compound  of  elbow  and  shoulder  joint  flexion.  After  tracing  the 
slit,  the  carbon  point  was  brought  back  to  the  initial  position  for 
the  respective  magnitude  and  after  an  interval  of  two  seconds  an 
effort  was  made  to  reproduce  the  magnitude,  the  cardboard  strip 
having  been  removed  by  the  operator  and  the  carbon  point  writing 
on  the  smooth  white  paper.  After  another  interval  of  about  two 
seconds,  a  second  attempt  was  made,  in  which  the  observer  estimated 
the  probable  or  apparent  error  of  his  first  trial  and  tried  to  repro- 
duce the  original  magnitude  more  exactly. 

TABLE    VI 
Error  of  Reproduction,  First  and  Second  Trials  and  their  Average 


"3 

•s 

10 

20 

30 

40 

50 

60 

70 

o 

C.E.    V.E. 

C.E.    V.E. 

C.E.    V.E. 

C.E.    V.E. 

C.E.    V.E. 

C.E.    V.E. 

C.E.    V.E. 

R. 
B. 

c. 

1 

2 
Av. 

1 

2 
Av. 

1 

2 

Av. 

+2      2 
+4      3 
+3      2.5 

+5      2 
+6      3 
+5.5   2.5 

+3      4 
+1       3 
+2      3.5 

+  25 

+  65 
+  45 

+  7     5 
+10     5 
+  8.5  5 

+  24 
+  24 
+  24 

0       6 

+5       6 
+2.5    6 

+3       6 
+5       5 
+4      5.5 

+2       6 
+4      6 
+3       6 

4       6 
+1       8 
—1.5    7 

+2      5 
+5       5 
+3.5   5 

—5      6 

+1       7 
—2       6.5 

—6       6 

—3       8 

4.5    7 

+  1       5 
+  4       6 
+2.5    5.5 

—2      6 
+1       9 
—  .5    7.5 

—13      8 

—  68 

—  9.5  8 

—  35 

—  18 

—  28 

—  65 

—  67 

—  6      7.5 

—16      7 
—12      8 
—14      7.5 

—  8      <9 
-  3      7 

—  5.5  7.5 

—12      9 
-10      8 
—11      8.5 

Av. 

+3.5    2.8 

+  4.8  4.6 

+3.2   5.8 

0       6.3 

—  .8    6.6 

—  5.8  7.8 

—10.2  7.8 

At  a  given  sitting  but  one  section.  A,  B  or  C,  was  used,  each  of 
the  seven  magnitudes  being  presented  in  chance  order,  but  no  magni- 
tude being  repeated  until  all  of  the  others  of  the  series  had  been 
presented.  Twenty-five  trials  for  each  magnitude  were  taken, 
making,  with  the  corrective  attempts,  fifty  reproductions  for  each  of 


26 


THE    INACCURACY    OF    MOVEMENT 


the  twenty-one  standards,  a  total  of  1,050  movements  for  each  sub- 
ject. Three  subjects  were  used,  all  being  graduate  students  in 
psychology,  two  of  them  ignorant  of  the  purpose  of  the  experiment, 
and  all  three  ignorant  of  the  results  from  day  to  day. 


TABLE    VII 
Erroe  of  Reproduction 


m 

[3 

30 

50 

70 

90 

110 

130 

150 

o 

C.E.    V.E. 

C.E.     V.E. 

C.E.    V.E. 

C.E.      V.E. 

C.E.      V.E. 

C.E.      V.E. 

C.E.      V.E. 

R. 
B. 
C. 

\ 

Av. 

1 

2 
Av. 

1 

2 

Av. 

+  1     4 
+  55 
+  3      4.5 

+  86 

+12      6 
+10      6 

+  6      7 
+  79 
+  6.5  8 

+    1         8 

+  5        9 
+  3        8.5 

+  9     11 
+16     10 
+12.5  10.5 

0        7 
+  3        8 
+    1.5     7.5 

—8       10 
+2        9 
—3        9.5 

^-3   13 

+5      13 
+4     13 

+3       8 
+5        5 
+4        8.5 

—10        8 

—  7       10 

—  8.5      5 

—  3         9 

—  1      14 

—  2      11.5 

—  1         5 

—  2        8 

—  1.5     <? 

—20      11 
—15         5 
—17.5    10 

—10       if 
9          g 

—  9.5    iO.5 

—  6      10 

—  5      i^ 

—  5.5    12 

—29        7 

-27        5 
—28        7.5 

—14      i;? 
-11       12 
—12.5    if 

—14      i^ 
—16      11 
—15       if.5 

—18.5    10.7 

-30       11 
—30       i(9 
—30       iO.5 

—15       12 
—14      i^ 
-14.5    13 

—14      i.^ 
—17      i^ 
—15.5    14 

Av. 

+  6.5  6.2 

+  5        8.8 

+1.7  m5 

—  4        5.5 

—10.8    iO.5 

—20      if.5 

TABLE    VIII 

Error  of  REPRODUCTioisr 


K 

[3 
H 

70  mm. 

100  mm. 

130  mm. 

160  mm. 

190  mm.      1     220  mm. 

250  mm. 

o 

C.E.      V.E. 

C.E.      V.E 

C.E.      V.E. 

C.E.     V.E. 

C.E.      V.E.     C.E.      V.E. 

C.E.     V.E. 

R. 
B. 
C. 

1 

2 
Av. 

1 

2 

Av. 

1 

2 

Av. 

+  14          9 
+29      if 
+  22       11 

+  10       ii 

+17     if 

+13.5    11.5 

+12        ,? 
+17       11 
+14.5      5.5 

0        10 
+11       12 

+  5.5  ii 

+10         5 

+14        5 
+12        5.5 

+  8       11 
+14       i5 
+11       13 

—12       10 

0      io 

—  6       10 

—  1      14 

—  1       12 

—  1     iJ 

+  3      14 
+  7      11 
+  5       12.5 

—23      13 

—17      12 
—20      if.5 

-16      15 
—19     i.4 

—17.5  i.4.5 

—  8     i.^ 

—  2     14 

—  5     14 

—37       11 
—30       16 

—33.5  13.5 

-16     i.^ 
—17     12 
—16.5  i5 

-15     ii 
-12     14 
—13.5  if.5 

—53     i5 
—55      15 

—54      i5 

—25      14 
—32      i5 
—28.5  i(5.5 

—33      18 
—32      i5 
—32.5  18 

—68      19 
—73     i5 
—70.5  17 

—38     i5 
—42      i5 
—40      18 

-45     i5 

—47      16 
—46      i5.5 

Av. 

+16.5   10.5+  9.5    iO..? 

—    .6  ii.5 

—14.2  13.7 

—21.2  13    —38.3  i6.5 

—52.2  i7 

Tables  VI.,  VII.  and  VIII  show  the  results  for  sections  A,  B 
and  C  for  the  three  subjects,  including  the  constant  error  and  vari- 
able error  of  both  the  first  and  the  corrective  trials,  and  the  average 
constant  error  and  variable  error  of  the  two  trials,  for  each  subject, 
along  with  the  grand  averages  for  all  three  subjects.  The  unit 
throughout  is  the  millimeter. 

The  results  are  thoroughly  clear  and  uniform.  In  every  section 
employed  we  find  the  relatively  small  magnitudes  reproduced  too 
great,  and  the  greater  magnitudes  reproduced  too  small,  both  in  the 
first  and  in  the  corrective  attempts,  while  there  is  a  region  of  in- 


THE    INDIFFERENCE    POINT  27 

difference  at  about  the  middle  of  each  section.  Moreover,  in  the 
case  of  the  small  magnitudes  the  positive  error  in  the  corrective 
attempts  is  seen  to  be  greater,  in  24  averages  out  of  the  26  in  which 
the  first  error  was  positive,  than  the  first  error.  The  difference 
ranges  in  section  A  from  1  to  3  mm.  (with  average  of  2^,  in  B  from 
1  to  7  mm.  (with  average  3^),  and  in  C  from  3  to  15  mm.  (with 
average  7^). 

But  in  the  case  of  the  larger  magnitudes  we  find  that  only  in 
10  cases  out  of  the  37  averages  in  which  the  constant  error  is  negative 
is  the  corrective  error  still  more  negative  than  the  first.  Of  these 
cases,  7  come  in  section  C,  which  contained  the  greater  magnitudes. 
Thus,  in  27  averages  out  of  37,  although  the  constant  error  was 
always  negative,  the  correction  was  positive,  just  as  in  the  cases 
of  the  positive  constant  errors.  These  corrective  attempts  were 
introduced  in  order  to  see  if  there  might  not  be  an  attenuation  of 
accuracy,  by  virtue  of  the  mere  repetition  of  the  process  of  judgment, 
the  positive  errors  being  thus  made  more  positive  and  the  negative 
more  negative.  But  this  is  not  the  case.  Instead  all  errors  tend, 
on  the  whole,  to  become  more  positive,  the  tendency  being  more  pro- 
nounced, however,  in  the  case  of  errors  already  positive.  It  is 
probable,  consequently,  that  this  effect  has  nothing  to  do  with  the 
particular  illusion  which  we  are  studying.  The  phenomenon  is 
probably  simply  a  "warming  up"  effect,  the  second  movement 
being  easier  than  the  first  by  virtue  of  the  motor  inertia  having 
already  been  overcome.  This  would  tend  to  make  the  corrective 
movement  really  greater  than  it  appeared.  In  the  case  of  the 
first  attempts,  then,  this  fact  would  also  have  some  bearing.  It 
would  mean  that  the  negative  errors,  so  far  as  actual  judgment  is 
concerned,  are  really  greater,  that  is,  more  negative  than  they  seem 
to  be  in  measurement  by  an  objective  scale,  and  that  the  positive 
errors,  similarly,  are  not  really  quite  so  great  as  measurement  shows 
them  to  be. 

Turning  now  to  the  real  point  of  the  experiment,  we  find  in  sec- 
tion A  (10-70  mm.),  for  the  three  subjects,  an  average  I.P.  at  about 
40  mm.;  in  section  B  (30-150  mm.),  an  I.P.  at  about  75  mm.,  and 
in  section  C  (70-250  mm.),  an  I.P.  at  about  125  mm.  By  some 
singular  coincidence  the  ratio  of  the  approximate  I.P.  to  the  upper 
magnitude  of  each  section  is  in  every  case  almost  exactly  one  half. 
It  is  apparent  that  in  extent  of  movement  and  in  time  of  movement, 
so  far  as  time  is  a  function  of  extent,  we  can  find  an  I.P.  at  what- 
ever point  we  choose.  Given  the  series  of  magnitudes  with  which 
we  are  to  work,  we  may  be  quite  certain  that  our  region  of  indif- 


28 


THE   INACCURACY    OF    MOVEMENT 


ference  will  fall  at  about  the  mid-point  or  region  of  the  particular 
scale.  Thus  in  the  present  experiment  we  tind  that  70  mm.,  which 
is  always  underestimated  in  section  A,  falls  within  the  region  of 
indifference  in  section  B,  and  is  always  overestimated  in  section 

C,  etc. 

TABLE    IX 
Eeeob  of  Repeoduction  for  Isolated  Magnitudes 


10  mm. 

70  mm. 

250  mm. 

Ist. 

2d. 

Av. 

1st. 

2d. 

Av. 

1st. 

2d. 

Av. 

C.E. 

—  .6 

—  .3 

—  .5 

+1.5 

+4.6 

+3 

—  .7 

—2.4 

—1.5 

R. 

V.E. 

1.6 

1.5 

1.5 

6.6 

6 

6.3 

12.3 

15.3 

13.8 

+ 

11 

13 

24 

11 

13 

24 

11 

13 

24 

14 

12 

26 

14 

12 

26 

14 

12 

26 

C.E. 

+  .3 

+3 

+3 

+2 

+2 

+2 

—3 

—5 

—4 

B. 

V.E. 

1.8 

1.5 

1.7 

4.^ 

5 

4.6 

12 

11 

12 

+ 

24 

23 

47 

14 

14 

28 

10 

8 

18 

1 

2 

3 

11 

11 

22 

15 

17 

32 

C.E. 

—  .2 

—  .3 

—  .3 

—2 

+2 

0 

—2 

—4 

—3 

P 

V.E. 

1.5 

1.3 

1.4 

6.7 

6.3 

6.5 

19 

23 

21 

V. 

+ 

14 

13 

27 

12 

13 

25 

12 

14 

26 

11 

12 

23 

13 

12 

25 

13 

11 

24 

A  second  experiment,  performed  as  a  check  to  the  preceding, 
shows  the  facts  still  more  clearly.  About  four  months  after  the 
sectional  records  had  been  taken,  the  three  magnitudes,  10  mm., 
which  had  always  been  affected  with  a  positive  constant  error,  70 
mm.,  which  fell  now  into  a  positive  error,  now  into  the  I.P.  and 
now  into  a  negative  error,  and  250  mm.,  which  was  always  under- 
estimated, were  used  singly  and  on  occasions  several  days  apart, 
after  the  same  method.  Table  IX.  shows  the  results  for  the  three 
subjects,  giving  the  constant  and  variable  errors  for  the  first  and 
the  corrective  trials,  and  their  average,  together  with  the  number 
of  positive  and  negative  errors  in  each  case.  Comparing  these 
constant  errors  with  those  of  the  same  magnitudes  in  the  previous 
experiment,  the  effect  of  inclusion  in  a  series  is  evident.  The  magni- 
tude 10  mm.,  always  overestimated  from  2  to  6  mm.  in  section  A, 
is  here  slightly  underestimated  (from  .2  to  .6  mm.  in  the  case  of 
the  two  subjects  who  knew  nothing  of  the  purpose  and  results  of  the 
experiment),  and  it  will  be  seen  that  this  constant  error  is  a  purely 
chance  one,  since  the  number  of  positive  and  negative  errors  is 
almost  equal — 51  positive  and  49  negative.  The  magnitude  70  mm., 
with  average  constant  error  of  — 10  mm.  in  section  A,  -[-  1-'^  mm. 
in  section  B,  and  -j-  16.5  mm.  in  section  C,  when  taken  by  itself 
has  a  constant  error  that  is  purely  accidental,  the  -[-  and  —  cases 


THE   INDIFFERENCE   POINT 


29 


being  here  also  almost  equally  divided,  25  +  and  25  —  in  the  case 
of  C,  24  4-  and  26  —  in  the  case  of  R.,  and  28  +  and  22  —  in 
the  case  of  B.,  with  average  constant  errors  of  0,  -|-  ^  and  +  2. 
The  magnitude  250  mm.  shows  the  same  results,  although  the  calcu- 
lated constant  error  is  slightly  negative  in  all  cases  (grand  average, 
—  2.8  mm.).  The  -|-  and  —  cases  show  the  same  equal  and  chance 
distribution,  in  the  cases  of  C.  and  R.  50  +  and  50  — .  Only 
in  the  case  of  B.  is  there  the  slightest  deviation  from  this  rule. 
But  even  here  the  constant  error  for  10  mm.  is  only  -|-  3  mm.  as 
against  -f-  5.5  mm.  in  section  A,  that  for  70-mm.  only  -\-  2  mm.  as 
against  -|-  13.5  mm.  in  section  B,  while  that  for  250  mm.  is  —  4  mm. 
as  against  —  40  mm.  in  section  C. 


rXSO 


Fig.   1.     Showing  the  Rise  of  the  Indifference  Point  with  the  Extension 
of  the  Series  Limits. 


This  conclusion  is  further  justitied  by  an  interesting  variation 
of  the  experiment,  performed  with  another  subject  (Hp.)  who  was 
ignorant  of  the  purpose  and  previous  conduct  of  the  experiment  as 
well  as  of  the  general  subject  of  the  indifference  point.  A  set  of 
standard  magnitudes  was  prepared  ranging  from  10  mm.  to  60  mm. 
by  increments  of  10  mm.,  from  60  mm.  to  150  mm.  by  increments 
of  15  mm.,  and  on   to  250  nim.   by  increments  of  20  mm.      The 


30  THE   INACCURACY    OF    MOVEMENT 

standards  of  series  10-60  were  now  given  and  reproduced  in  chance 
order,  five  trials  being  made  of  each  magnitude,  a  total  of  30  trials. 
At  this  point,  without  the  knowledge  of  the  subject,  the  next  magni- 
tude (75)  of  the  series  was  introduced,  and  again  five  trials  made 
of  each  standard.  Then  the  next  magnitude  was  introduced  and 
similar  tests  made  for  series  10-90.  This  process  was  continued 
until  all  the  higher  magnitudes  of  the  series  had  been  introduced, 
the  last  set  thus  consisting  of  five  trials  for  each  magnitude  of  the 
total  series  10-250.  This  made  a  total  of  690  movements.  All 
these  trials  were  made  at  a  single  sitting,  so  that  the  subject  worked 
with  a  gradually  expanding  series,  the  lower  limit  of  which  re- 
mained constant  while  the  upper  limit  increased  by  regular  and 
approximately  equal  steps. 

The  results  are  shown  in  Fig.  1.  In  set  1  the  series  breaks,  as 
usual,  approximately  half  way  between  the  two  extremes,  giving 
an  I.P.  at  35  mm.,  with  positive  constant  errors  below  and  negative 
above.  In  set  2  the  I.P.  rises  to  about  40  mm.,  in  set  3  to  45  mm., 
in  set  4  to  50  mm.,  and  similarly  throughout  the  whole  experiment 
(disregarding  the  exceptional  height  of  the  I.P.  for  range  0-150), 
each  new  standard,  as  it  is  introduced,  being  found  to  influence  the 
apparent  magnitude  of  every  other.  The  general  effect  of  this 
influence  is  to  increase  all  positive  errors.  This  increase  shows 
itself  in  three  ways:  (1)  "When  the  C.E.  was  positive  from  the 
beginning,  this  error  is  seen,  on  the  whole,  to  increase  with  the  in- 
troduction of  each  new  standard.  Thus  the  positive  C.E.  for  10 
mm.,  at  first  8.4,  becomes  as  great  as  13.6,  that  for  20  mm.  increases 
from  3.8  to  14.8,  and  that  for  30  mm.,  from  1  mm.  to  10.8.  (2) 
Constant  errors  which  were  in  the  beginning  negative  undergo  a 
transformation  in  the  course  of  the  experiment.  Each  decreases 
in  magnitude  through  an  indifference  point  of  its  own,  below  which 
it  emerges  as  a  positive  error.  This  is  shown  in  the  case  of  all 
standards  from  40  mm.  through  120  mm.  (3)  As  a  result  of  these 
transformations  the  region  of  indifference  varies  about  a  constantly 
augmenting  magnitude  which  ranges  from  35  mm.  to  100  mm.,  but 
goes  in  two  cases  as  high  as  110  mm.  and  120  mm.  In  general,  the 
indifference  point  rises  in  response  to  the  extension  of  the  series  at 
its  upper  limit,  and  lies,  in  all  cases,  at  a  point  which  represents 
roughly  the  median  of  the  total  group  of  magnitudes. 

The  results  of  all  three  experiments  are  consistent,  and  afford 
the  following  answers  to  four  of  our  introductory  questions.  (1) 
A  periodic  I.P.  can  be  found  within  the  total  series  {S)  by  working 
with  its  special  sections  (A,  B  and  C).  (2)  The  same  absolute 
magnitude  may  be  under  one  circumstance  an  I.P,,  under  another. 


TEE    INDIFFERENCE    POINT  31 

effected  with  a  positive  C.E.  or  again  with  a  negative  C.E.  (3) 
The  gradual  extension  of  the  series  limits  is  accompanied  by  a  corre- 
sponding shift  in  the  region  of  indifference.  (4)  No  magnitude 
evinces  any  C.E.  when  estimated  out  of  relation  to  a  series  or  group 
of  which  it  is  a  member.  (5)  The  reply  to  the  fifth  question  is  to 
be  found  in  the  tables  of  Chapter  V.,  in  which  are  shown  the  effect, 
on  the  direction  and  magnitude  of  errors  of  reproduction,  of  length- 
ening the  interval  between  standard  and  reproduction.  This  pro- 
cedure has  the  effect  of  extending  the  period  of  time  within  which 
the  individual  members  of  the  series  occur.  We  have  found  that 
in  the  case  of  2-sec.  intervals,  with  such  series  as  were  used  in  the 
present  experiment,  the  influence  of  the  judgments  of  one  magni- 
tude persists  throughout  the  experiment,  affecting  in  a  very  definite 
manner  the  judgments  of  all  other  magnitudes.  Our  present  query 
is  concerning  the  persistence  time  of  such  an  influence.  In  the 
experiments  of  Chapter  V.  intervals  of  2,  5,  10,  15  and  30  seconds 
were  introduced  between  the  standard  and  the  reproduction.  These 
experiments  afford  somewhat  definite  answer  to  our  question.  In 
Table  XII.,  recording  the  errors  in  reproduction  of  extent  for 
observer  W.,  the  I.P.  is  found  in  all  series  up  to  the  15-sec.  interval. 
When  intervals  of  30  sec.  are  employed  the  C.E.'s  are  all  consid- 
erably negative  and  the  group  effect  is  not  found.  In  Table  XV., 
recording  the  error  in  the  reproduction  of  duration  for  the  same 
observer,  the  I.P.  appears  after  2-sec.  and  5-sec.  intervals,  but  not 
beyond,  while  in  similar  experiments  on  observer  H.  (Table  XVI.) 
the  I.P.  is  found  only  after  intervals  of  2  sec.  While  these  are  but 
incidental  observations  and  can  not  be  said  to  serve  as  basis  for  any 
adequate  quantitative  statement,  there  is  evident  indication  that  the 
constant  errors  do  not  so  much  represent  transformations  in  a 
memory  image  of  the  stimulus  in  question  as  they  do  the  effect,  on 
a  present  judgment,  of  the  persistence  of  the  mental  set  involved 
in  a  previous  judgment.  If  the  interval  between  the  two  judgments 
is  sufficient,  the  first  disposition  is  soon  dissipated  and  is  no  longer 
adequate  to  affect  the  second  performance.  That  the  C.E.  is  not 
due  to  the  transformation  of  a  memory  image  is  apparent  from  the 
fact  that  in  this  case  no  C.E.  appears. 

I  conclude  then  that  the  phenomenon  of  the  indifference  point, 
.so  far  as  it  occurs  in  our  spatial  judgments,  and  in  our  temporal 
judgments  so  far  as  they  are  a  function  of  the  extent  of  movement, 
is  of  purely  central  origin,  and  that  its  position  depends  entirely 
upon  the  range  or  limits  of  the  magnitudes  in  question. 

The  suspicion  is  a  natural  one  that  the  varying  and  contradictory 
I.P. 's  found  by  the  investigators  of  the  time-sense  were  due  to  dif- 


32 


TEE   INACCURACY    OF    MOVEMENT 


ferences  in  the  limits  of  the  series  of  magnitudes  employed.  And 
if  the  actual  range  of  magnitudes  used  be  but  tabulated  alongside 
the  I.P. 's  obtained,  the  suspicion  is  strikingly  sustained.  In  many 
cases  the  range  of  magnitudes  actually  used  is  not  clearly  stated, 
nor  is  it  always  clear  how  much  of  the  total  range  was  used  at 
a  given  sitting.  Such  data  as  could  be  found  from  those  who 
particularly  studied  the  constant  error  have  been  tabulated  in  the 
following. 

TABLE    X 
Relation  of  I.P.  to  Range  of  Intervals 


Investigator 

I.  P.,  in  Seconds'^ 

Range,  in  Seconds 

Vierordt. 

Subject  N. 

1.5 

.5    to    5.8 

"       H. 

1.4 

1       to    3.5 

"       V. 

3 

.6    to    3.5 

Touch. 

2.5 

.25  to    5 

Hearing. 

3.5 

.5    to    8 

Spontaneous  movement. 

5 

.2    to  65 

Horing. 

.5 

.3    to    1.4 

Kollert. 

.8 

.4    to    1.8 

Estel. 

Multiples  of  .75 

Used  different  sections  of  range  1.5 
to  8  at  different  parts  of  day. 

Glass. 

2  to  5 

.7    to  15 

3 

.7    to    9 

Stevens. 

.7 

.2    to    3 

One  would  scarcely  pretend  to  submit  these  figures  to  a  thor- 
oughgoing comparison,  because  the  methods  and  apparatus  were 
extremely  varied,  and  the  subjects  as  well  as  the  operators  were  all 
different.  Moreover,  the  influence  on  the  I.P.  need  not  be  sup- 
posed to  be  directly  proportional  to  the  quantitative  shift  in  the 
series  limits.  Nevetheless  the  table  is  suggestive.  Vierordt,  for 
instance,  states,  on  the  basis  of  the  averages  quoted  in  the  above 
table,  that  the  I.P.  "depends  especially  on  the  sense  under  investi- 
gation," and  finds  that  for  touch  the  I.P.  falls  at  2.5  sec,  for  hearing 
at  3.5,  and  for  the  time  of  spontaneous  movements  at  5  sec.  But 
another  fact  should  be  observed  which  Vierordt  failed  to  point  out, 
viz.,  that  for  touch  the  range  of  intervals  employed  was  .25  to  5.0 
sec,  for  hearing  .5  to  8  sec.  and  for  movement  .2  to  65  sec.  In  the 
light  of  the  results  we  have  just  reported  it  is  extremely  probable 
that  the  variation  of  the  I.P.  is  much  more  a  function  of  the  range 
of  intervals  employed  than  of  the  ' '  sense  under  investigation. ' '  For 
in  every  case  the  region  of  indifference  approximates  the  middle 
of  the  range.^^ 

^^  In  the  case  of  the  spontaneous  movements  only  216  out  of  1,708  move- 
ments were  over  20  seconds  in  duration,  and  only  444  of  the  upper  third  of  his 
scale  contrast  witli  757  movements  in  the  lower  third.  The  I.P.  would  probably 
have  been  still  higher  here  if  both  ends  of  the  scale  had  been  equally  employed. 


TEE    INDIFFERENCE    POINT  33 

Similarly,  Horing,  with  a  range  of  .3  to  1.4  sec,  finds  his  I.P. 
at  .5  see.,  Kollert,  with  a  range  of  .4  to  1.8  sec,  finds  a  higher  I.P., 
and  Stevens,  with  range  .2  to  3  sec,  finds  it  to  be  at  .7  sec,  while 
Glass,  using  range  .7  to  9  sec,  finds  it  at  3  sec,  although  for  range 
.7  to  15  sec  it  rises  as  high  as  5  sec  With  these  facts  in  mind 
little  stock  can  be  taken  in  the  reports  of  rhythmic,  oscillating, 
periodic  indifference  points,  unless  it  is  explicitly  stated  just  what 
range  of  intervals  was  employed,  not  merely  in  the  experiment  as 
a  whole,  but  at  each  sitting  from  w^hich  results  are  used.  Estel,  who 
found  periodic  I.P.  in  his  total  scale,  employed  different  sections 
of  this  scale  at  different  sittings.  Shaw  and  Wrinch,^'  who  used  the 
method  of  successive  reproduction,  thus  partially  eliminating  the 
effect  of  range,  do  not  state  the  order  in  which  the  different  intervals 
were  used.  Negative  errors  were  found  for  .5,  .75  and  1.5  seconds. 
Records  on  four  subjects,  using  intervals  ranging  from  .9  to  10 
seconds,  did  not  agree. 

Theoretical. — The  cause  of  this  tendency  to  positive  and  negative 
constant  errors  at  the  two  extremes  of  a  scale  of  magnitudes  has 
always  remained  obscure.  At  first  thought  it  seems  to  be  but  an 
instance  of  Fechner's  time-error,  with  an  unexplained  difference  in 
direction  at  the  two  ends  of  the  scale.  But  that  the  illusion  is  not 
based  on  the  temporal  positions  of  the  two  stimuli  is  clear  from  the 
fact  that  it  does  not  occur  when  the  magnitudes  are  taken  singly, 
although  the  temporal  positions  of  standard  and  reproduction  remain 
unchanged.  Schumann  attributed  the  phenomenon,  in  the  ease 
of  time,  to  mechanical  sources  of  error  in  the  apparatus.  But  this 
could  hardly  explain  the  same  tendency  in  judging  intensity  of 
light  (Leuba,  Lewis),  or  the  size  of  squares  (Kennedy)  or  visual 
lines  (]\Iiinsterberg).  Vierordt's  suggestion  was  that  it  might  be 
due  either  to  the  peculiarity  of  the  sense  organ  or  to  the  accom- 
panying psychical  processes.  Delabarre,^"  working  with  extent  of 
movement,  offers  various  explanations,  none  of  which  seem  adequate. 
The  first  suggestion  is  the  lack  of  proper  and  sufficient  current  con- 
trol in  performing  the  short  movements.  The  reproduction  of' the 
short  movements  is  thus  rougher,  and  the  moving  member  can  not 
be  stopped  at  will.  This  is  probably  the  case  with  the  very  small 
movements,  but  possibility  of  current  control  would  seem  to  be  a 
rather  fixed  physiological  factor  and  not  to  vary  up  and  down  the 
scale  of  extension.  This  it  must  do  if  it  is  to  account  for  the  fact 
that  a  relatively  large  movement,  underestimated  in  one  series,  is 
overestimated  when  placed  in  another  series.      The  same  criticism 

"Univ.  of  Toronto  Studies,  1,  105,  1900. 
'^Op.  cit.,  89. 


34  TEE   INACCURACY    OF    MOVEMENT 

also  applies  to  his  statement  that  these  small  movements  are  unusual 
and  hence  overestimated.  Actually,  movements  so  small  as  writing 
movements  are  not  at  all  unusual,  and  are  made,  moreover,  with 
considerable  precision,  while  we  found  movements  of  a  foot  or  more 
being  overestimated.  Slower  speed  for  the  long  movements  is  also 
suggested.  While  this  might  apply  to  the  greater  extents,  it  has  no 
value  for  the  cases  of  the  other  senses,  in  which  the  time  element  is 
not  involved.  In  the  same  way  objection  must  be  made  to  the 
theory  that  the  effect  of  the  constant  change  and  renewal  of  the 
motor  impulse  is  to  increase  the  apparent  magnitude  of  the  large 
movements.  Besides,  all  these  points  apply  to  the  standard  move- 
ment as  well  as  to  the  reproduction,  and  do  not  make  clear  why  one 
should  be  affected  in  judgment,  the  other  not. 

Wundt  considers  the  tendency  to  overestimate  small  articular 
movements  and  to  underestimate  large  ones  as  a  tactual  analogue 
of  the  similar  illusion  present  in  the  estimation  of  visual  angles. 
''This  comes  under  the  general  principle  that  a  relatively  greater 
expenditure  of  energy  is  required  for  a  short  movement  than  for  a 
more  extensive  one,  because  it  is  relatively  more  difficult  to  begin 
a  movement  than  to  continue  it  after  it  is  started.""^  If  it  were 
merely  a  case  of  estimation  in  terms  of  an  objective  unit,  or  even  a 
case  of  the  comparison  of  two  arbitrarily  given  standards,  Wundt 's 
suggestion  might  suffice.  But  in  all  these  experiments  the  method 
of  reproduction  has  been  used.  The  observer's  task  was  not  the 
comparison  of  one  standard  with  another,  but  the  reproduction  of 
a  given  normal  stimulus,  and  it  was  this  reproduction  that  showed 
the  constant  error,  and  there  is  no  reason  for  supposing  the  ' '  relative 
difficulty"  of  a  short  movement  to  interfere  with  the  attempt  to 
reproduce  the  same  short  movement.  The  same  "relative  diffi- 
culty ' '  is  present  in  the  reproduction  as  in  the  standard. 

By  far  the  most  complete  discussion  of  the  positive  and  negative 
errors  and  the  resulting  indifference  point  in  the  field  of  movement 
is  to  be  found  in  AVoodworth's  chapter--  on  the  subject.  The  pos- 
sible efficient  causes  are  here  analyzed  into  motor  factors,  sensory 
factors,  emotional  factors  and  factors  of  attention  and  association. 
Under  motor  factors  are  included  the  facts  of  dynamogenic  stimula- 
tion and  fatigue.  If  we  suppose  that  the  first  small  movement  acts 
as  a  stimulant  to  the  motor  system,  the  reproduction  would  be  ex- 
pected to  show  the  effect  in  being  somewhat  more  easily  made,  hence 
probably  correspondingly  larger  than  necessary.      And  in  the  case 

=^1  Wundt,  "Outlines,"  3d  Eng.  ed.,  p.  139,  1907. 
"  "  Le  Mouvement,"  Chapt.  VI. 


THE    INDIFFERENCE    POINT  35 

of  the  negative  errors  it  might  be  supposed  that  the  longer  move- 
ments, instead  of  acting  as  stimulants,  actually  have  a  fatiguing 
effect,  so  that  their  reproductions  are  somewhat  more  difficult  and 
fall  short.  But  this  last  supposition  is  shown  to  be  "undoubtedly 
false,"  from  the  fact  that  a  single  contraction,  of  even  maximal 
force,  does  not  fatigue,  but  acts  as  a  stimulant  to  the  motor  appa- 
ratus. Besides,  the  illusion  does  not  become  more  pronounced  in 
the  course  of  the  experiment,  as  should  be  expected  on  the  basis  of 
fatigue.  Woodworth  admits  that  the  motor  factor  probably  helps 
to  produce  the  positive  error,  but  insists  that  this  factor  alone  is 
insufficient  to  explain  any  illusion  of  perception,  since  it  still  re- 
quires to  be  shown  why  the  error,  once  made,  is  not  perceived  and 
allowed  for. 

]\Ioreover,  in  the  light  of  the  present  experiment,  and  the  quoted 
results  of  many  others,  neither  the  stimulating  effect  of  the  small 
movements  nor  the  fatiguing  effect  of  large  ones,  nor  both  together, 
would  suffice  to  account  for  the  fluctuation  of  the  indifference  point 
with  the  change  of  series  limits.  It  is  hardly  possible  that  a  70-mm. 
movement,  taken  in  one  series,  should  be  physiologically  stimulating, 
in  another  of  slightly  different  range,  fatiguing,  while  in  still 
another  it  should  be  physiologically  indifferent.  For  the  same  rea- 
son the  exciting  or  depressing  emotional  effect  of  the  preceding 
movement,  while  it  might  be  conceived  as  contributing  to  the  total 
effect  if  the  indifference  point  were  found  to  be  fixed,  can  hardly 
be  supposed  to  possess  the  same  variability  as  is  found  in  the  indif- 
ference point. 

To  Woodworth,  "the  sensory  factor  in  the  genesis  of  the 
constant  errors  and  illasions  may  seem  the  only  one  worth  recog- 
nizing." Under  sensory  factors  he  includes  the  lack  of  adequate 
sensory  evidence  for  finer  discrimination  of  movements,  and  an 
inequality  of  peripheral  sensation,  shown  in  the  fact  that ' '  the  longer 
and  stronger  the  habitual  movements  of  a  member,  the  less  felt  are 
its  movements."  While  these  factors  seem  to  be  of  value  in 
accounting  for  asymmetrical  errors  and  in  comparison  of  movements 
in  different  directions  or  by  different  parts  of  the  body,  they  do  not 
seem  to  have  any  direct  bearing  on  the  question  of  the  variable 
indifference  poim.  Nor  do  they  apply  to  the  same  phenomenon  in 
other  senses,  in  which  the  factor  of  movement  is  not  present. 

The  fact  seems  to  be  rather,  that  the  phenomenon  of  the  indif- 
ference point  and  the  so-called  positive  and  negative  time  errors 
result  from  purely  central  factors.  The  general  law  seems  to  be 
that  in  all  such  estimates  we  tend  to  form  our  judgments  around 


36  THE   INACCURACY    OF    MOVEMENT 

a  mode  or  central  tendency  of  the  series.  Toward  this  mean  each 
judgment  tends  by  virtue  of  a  mental  set  corresponding  to  the 
particular  scale  or  series  in  question.  This  is  practically  the  equiva- 
lent, for  judgment,  of  Leuba's  "Law  of  Sense  Memory" — "There 
is  a  natural  tendency  in  us  to  shift  the  sensation  held  in  memory 
towards  the  middle  of  the  scale  of  intensities."^^  But  our  own 
results  seem  to  indicate  that  the  phenomenon  is  one  of  direct  per- 
ception rather  than  of  memory  as  such.  If  it  were  due,  as 
Wreschner,  Leuba  and  others  have  supposed,  to  changes  in  the 
memory  image  during  the  interval  between  the  standard  and  the 
comparison  or  reproduction  the  same  effect  should  be  present  when 
a  given  magnitude  or  intensity  is  investigated  alone — out  of  relation 
to  a  group  or  series.  The  present  experiments  show  that  this  is 
certainly  not  the  case  for  extent  of  movement  and  probably  not  for 
time.  Moreover  the  results  of  the  experiments  on  reproduction  of 
time  of  movement  indicate  that  it  occurs  only  when  the  interval 
between  standard  and  reproduction  is  short.  This  is  at  least  not 
the  most  favorable  condition  for  changes  in  the  memory  image. 
Besides,  if  the  illusion  is  due  to  such  changes,  it  is  not  clear  why 
the  behavior  of  the  memory  image  should  be  so  dependent  on  the 
general  range  or  group  in  which  the  impression  happened  to  occur. 
It  is  true  that  memory  images  undergo  changes,  which  depend 
chiefly  on  the  period  of  their  duration.  But  the  phenomenon  of 
the  indifference  point  can  not  be  brought  under  the  law  of  these 
changes.  The  constant  errors  flanking  the  indifference  point  seem 
rather  to  be  errors  of  direct  perception  and  their  generalization 
should  be  a  law  of  perception. 

In  the  case  of  immediate  estimation  at  least  it  is  not  so  much 
a  law  of  memory  as  a  law  of  judgment,  and  in  the  case  of  immediate 
reproduction,  a  correlative  law  of  automatic  tendency  in  perform- 
ance. It  is  the  operation  in  judgment  of  the  law  of  habit  and 
adaptation.  Just  as  a  group  of  diverse  and  varying  movements 
directed  towards  a  given  end  gravitate  toward  an  average  perform- 
ance which  will  economize  effort  and  yet  accomplish  the  end  of  the 
activity,  so  the  act  of  judgment,  in  the  interest  of  mental  economy 
—  and  especially  the  motor  process  of  reproduction,  when  that  method 
of  registration  is  employed — tends  toward  an  average  estimate.  It 
is  probable  that  even  when  single,  unserial  stimuli  are  received  or 
movements  made,  they  are  "apperceived"  into  pretty  definite  men- 
tal sets  or  sense  categories.  Thus  our  movements  do  not,  in  their 
extent  and  force,  form  a  serial  scale  or  continuum,  but  fall  apart 

^'  Op.  cit. 


THE    INDIFFERENCE    POINT  37 

into  rough  groups,  with  rather  indefinite  limits  but  with  rather 
definite  central  tendencies — such  groups,  for  instance,  as  writing 
movements,  eating  movements,  dressing  movements  or  various  sets 
of  trade  and  professional  movements  depending  on  one's  habits  and 
customary  occupation.  And  the  constant  errors  found  by  Delabarre, 
Loeb  and  others  when  movements  in  such  various  directions  and  of 
different  "category"  are  compared,  are  probably  due  to  just  these 
central  factors  of  the  judgment  of  magnitude  as  much  as  to  any 
anatomical  or  physiological  facts. 

What  we  have  here  is  somewhat  different  from  the  contrast  ex- 
perience. The  apparent  magnitude  of  one  member  is  not  condi- 
tioned so  much  by  its  general  relation  to  other  members  of  the 
series  or  by  the  effect  of  an  inmiediately  preceding  member  as  by 
its  rather  specific  relation  to  the  central  tendency  or  mean  or  average 
of  the  series.  It  is  not  the  phenomenon  of  contrast.  In  fact  it  is 
just  the  reverse,  for  the  law  of  contrast  would  tend  to  make  the 
small  magnitude  seem  still  smaller  in  the  presence  of  the  large  and 
the  large  seem  correspondingly  greater.  Nor  can  it  be  classified 
as  a  phenomenon  of  adaptation  of  attention  in  which  expectation 
or  surprise  are  supposed  to  result  in  constant  error  of  estimation. 
Adaptation  of  attention  toward  the  group  as  a  whole  would  lead 
to  a  situation  of  contrast.  The  small  magnitude  would  surprise 
by  its  unexpected  shortness  and  be  underestimated  in  reproduction, 
while  the  constant  error  for  the  greater  magnitudes  would  be  posi- 
tive. This  again  is  just  the  reverse  of  what  we  actually  find  in  the 
present  experiment. 

This  law  of  central  tendency  may  be  illustrated  in  the  case  of 
judgments  of  extent  of  movement  in  some  such  way  as  the  following. 
Suppose  AC  to  represent  a  scale  of  magnitudes  and  B  to  represent 
a  value  in  the  central  region,  between  A  and  C.  In  the  attempt, 
now,  to  reproduce  a  given  magnitude,  every  point  in  the  series  may 
be  said  to  exert  an  attraction  on  the  moving  member,  by  virtue  of 
the  automatic  character  of  motor  habit — the  thing  once  done  tends 
in  the  future  to  carry  itself  out  to  completion  whenever  it  is  initiated. 
As  a  result  of  this  "attraction"  the  tendency  to  reproduce  a  magni- 
tude larger  than  AB  is  partly  inhibited  by  the  tendency  to  make 
one  less  and  vice  versa.  B  thus  becomes  the  "indifference  point," 
and  AB  the  magnitude  whose  reproduction  will  be  least  disastrously 
affected  by  the  motor  habit.  In  Uk^  case  of  the  other  senses, 
though  not  reenforced  by  this  motor  hnv,  th(^  law  of  central  tend- 
ency in  judgmoif  prevails  nevertholcss  to  sufficient  extent  to  compli- 
cate our  measuiviiiciils  and  to  keep  ns  supplied  with  "problems." 


38  TEE    IX  ACCURACY    OF    MOV  EM  EXT 

For  the  same  rule  holds,  as  researches  referred  to  in  the  first 
part  of  the  chapter  have  shown,  in  cases  in  which  errors  of  repro- 
duction are  not  present,  cases,  i.  e.,  in  which  the  judgment  is  purely 
a  matter  of  comparison  of  sense  stimuli — visual  lines,  visual  angles, 
duration,  weight,  force,  brightness — all  show  the  same  phenomenon. 
The  law  of  central  tendency,  in  such  cases,  produces  results 
analogous  to  many  cases  of  "preperception. "  The  hunter  who 
mistakes  the  clump  of  stubble  for  a  rabbit  is  the  classical  example. 
He  is  mentally  set  for  "rabbits"  and  is  not  engaged  in  an  experi- 
ment on  sensible  discrimination.  Hence  small  differences  are  dis- 
regarded. Anything  which  roughly  approximates  the  form  of  a 
small  animal  is  adequate  to  provoke  the  judgment  "rabbit."  In 
ordinary  life  we  are  not  concerned  with  small  differences,  we  are 
more  occupied  with  averages,  types,  central  tendencies,  general 
resemblances.  It  is  this  fact  which  frequently  permits  even  a  crude 
counterfeit  to  pass  undetected.  Now  it  appears  that  this  daily 
habit  carries  over  even  into  our  deliberate  experiments  on  sensible 
discrimination.  Each  impression  leaves  a  mental  set  which  tends 
more  or  less  to  assimilate  a  succeeding  impression,  just  as  the  set 
corresponding  to  or  induced  by  the  idea  "rabbit"  tends  to  assimi- 
late the  clump  of  stubble.  Any  stimulus  not  too  different  is  likely 
to  appear  identical,  even  though  practised  scrutiny  with  knowledge 
of  results  might  make  the  discrepancy  apparent.  Now  it  is  easy 
to  see  why  the  resulting  mental  set  of  the  series  of  magnitudes, 
light  intensities,  for  example,  should  correspond  to  the  central 
tendency  of  the  series.  In  this  region  there  are,  in  both  directions, 
magnitudes  of  general  resemblance.  In  the  case  of  the  extreme 
magnitudes,  however,  the  resemblances  run  in  one  direction  only. 
In  the  central  region  the  stretches  or  ranges  of  resemblance  over- 
lap and  intensify  each  other,  magnitudes  within  them  are  mutually 
taken  for  each  other,  and  the  resultant  is  a  mental  set  for  the 
central  tendency.  Every  magnitude  tends  to  be  assimilated  by  this 
set  and  made  to  appear  less  different  from  the  central  tendency  than 
it  really  is.  The  degree  of  this  assimilation  is  measured  by  the 
amount  of  difference  required  to  do  violence  to  the  mental  set  in  a 
single  instance.  Thus,  in  the  case  of  the  hunter,  the  degree  of 
assimilation  is  measured  by  the  deviation  in  contour,  shading  and 
general  appearance  sufficient  to  provoke  a  judgment  of  "not  rabbit," 
in  the  inexact  discriminative  processes  of  a  hunter  intent  on  game. 
Just  less  than  this  amount  of  difference  will  ordinarily  go  unde- 
tected. Similarly,  in  the  case  of  light  intensities,  a  rather  definite 
degree    of    assimilation    affects   magnitudes    on   both    sides    of   the 


TEE   INDIFFERENCE   POINT 


39 


indifference  region.  This  amount  of  difference  is  ignored  in  the 
process  of  discrimination.  This  degree  of  assimilation  is  measured 
by  the  C.E.  This  of  course  will  be  negative  for  magnitudes  above  the 
region  of  indifference,  since  this  amount  of  difference  is  unnoticed. 
For  the  same  reason  the  C.E.  will  be  positive  for  magnitudes  below 
the  region  of  indifference,  i.  e.,  magnitudes  at  either  extreme  will 
tend  to  appear  more  nearly  equal  to  the  central  tendency  than 
they  really  are.  The  region  of  indifference  represents  the  range 
of  magnitudes  any  of  which  satisfies  the  general  mental  set  induced 
by  the  series  as  a  whole— they  can  be  roughly  substituted  for  each 
other  without  detection. 

In  this  sense  the  illusions  may  be  said  to  be  due  to  the  effect  of 
expectation,  except  that  in  this  case  expectation  results  in  assimila- 
tion instead  of  in  contrast.  The  words  ''mental  set  for  the  central 
tendency"  simply  mean  that  we  are  adjusted  for  or  tend  to  expect 
the  average  magnitude,  and  to  assimilate  all  other  magnitudes 
toward  it,  to  accept  them  in  place  of  it. 


CHAPTER    IV 

Relation  between  Extent  and  Dueation 

Many  hypothetical  attempts  have  been  made  to  simplify  the 
judgment  of  magnitude  in  the  case  of  movements  by  reducing  the 
various  perceptions  of  extent,  time,  force,  speed  and  position  to 
terms  of  one  or  more  of  these  factors.  Thus  it  has  frequently  been 
conjectured  that  the  judgment  of  extent  is  based  on  the  perception 
of  duration  or  on  the  force  of  contraction,  that  force  is  measured 
in  terms  of  extent  or  speed,  etc.  The  most  frequent  suggestion  has 
been  that  which  would  make  the  estimation  of  extent  a  function  of 
the  perception  of  time.  Loeb^  was  led  to  this  supposition  by  the 
observation  that  some  subjects  sought  to  attain  greater  accuracy 
by  counting  during  the  execution  of  the  movement.  But  the  records 
of  such  subjects  showed  no  superiority  over  those  in  whom  the 
tendency  w^as  not  remarked.  Kramer  and  ]\Ioskiewicz-  proposed 
the  same  reduction  as  a  result  of  their  experiments  on  the  Loeb 
illusion  already  quoted.  They  supposed  that,  especially  in  the 
presence  of  such  different  sensation  complexes  as  were  involved  in 
their  experiments,  the  only  quality  common  to  the  two  movements 
was  the  element  of  time  and  that  the  durations  of  these  intospectively 
equal  extents  would  be  found  to  agree.  The  conjecture,  however, 
was  not  put  to  the  test.  Similarly  Jaensch,^  working  on  the  same 
problem  very  recently,  finds  that  times  agree  much  more  closely 
than  extents  though  the  errors  are  not  always  in  the  same  direction. 
In  fact  he  finds  the  time  differences  to  be  as  small  as  one  could 
expect  even  in  deliberate  attempts  to  reproduce  durations,  and  con- 
cludes that  "we  hold  stretches  to  be  equal  the  retrospective  times 
of  which  are  equal."  Even  when  the  movements  were  made  from 
the  same  initial  point  the  times  were  almost  equal  and  seemed  to 
serve  as  criteria  when  visual  data  were  excluded.  Kiilpe,  while  not 
adhering  to  a  strict  duration  theory,  says  that  "as  a  general  rule  the 
apparent  magnitude  of  a  distance  is  proportional  to  the  length  of 
time  required  for  movement  across  it." 

On  the  other  hand  we  find  an  array  of  objections  accumulated 
by  Woodworth*  which  seems  to  discredit  completely  the  foregoing 
hypotheses.      Chief  among  these  objections  are  the  following: 

^  Pfliiger's  Arch.,  41,  124,  1887. 
^  Op.  cit.,  125. 

"Zeit.  f.  Psychol.,  41,  257-279,  1905. 

*"Le  Mouvement,"  Ch.  IV.     "  Acciiracy  of  Voluntary  Movement,"  77  ff. 

40 


RELATION    BETWEEN    EXTENT    AND    DURATION  4I 

1.  The  time  of  movements  may  be  extremely  varied  without 
entirely  destroying  the  approximate  equality  of  their  extents. 

2.  The  results  obtained  by  Cattell  and  Fullerton  show  that  extent 
can  be  judged  better  than  time. 

3.  Although  the  constant  error  when  one  movement  is  made 
faster  than  another  is  iii  the  direction  of  compensation  it  is  not 
sufficient  for  it. 

4.  If  we  judged  by  time  alone  the  difference  between  long  and 
short  or  fast  and  slow  movements  would  have  no  meaning  for  us 
aside  from  terms  of  visual  space  or  of  force. 

5.  There  is  no  a  priori  reason  for  believing  any  one  perception 
to  be  more  fundamental  than  others.  The  sensations  of  movement 
are  varied  enough  to  afford  each  sort  of  judgment  a  sensory  basis 
of  its  own.  Introspectively  there  seems  to  be  no  inference  from 
one  perception  to  another. 

But  Woodworth  points  out  the  need  of  more  and  crucial  experi- 
mental data  on  the  precise  relation  between  the  two  factors  and 
suggests  the  three  following  methods  of  procedure : 

1.  Confusion  of  the  supposed  primitive  perception.  The  other, 
if  derived,  should,  under  such  circumstances,  be  less  accurate  than 
ordinarily. 

2.  The  method  of  correlation  or  of  incidental  observation  of  one 
factor  while  the  observer  is  occupied  with  the  other. 

3.  Separate  accuracy  tests.  No  purely  derivative  perception 
should  be  found  to  be  more  accurate  than  the  more  primitive  per- 
ception on  which  it  is  based.  It  should,  indeed,  be  less  accurate, 
since  the  process  of  derivation  would  probably  introduce  additional 
errors. 

The  first  method  here  suggested  has  frequently  been  applied  and 
has  resulted  in  considerable  irregular  but  incommensurate  disturb- 
ance of  the  presumably  derived  perception.  The  chief  difficulty  with 
the  second  method  seems  to  have  been  that  of  arranging  apparatus 
which  would  register  simultaneously  the  extent  and  duration  of 
movements  of  any  considerable  magnitude.  The  method  appears 
not  to  have  been  employed  until  the  experiments  of  Jaensch,  and 
these  were  under  restricted  conditions  and  with  unsatisfactory^  appa- 
ratus. The  apparatus  used  in  the  present  research  is  peculiarly 
adapted  to  such  procedure,  and  in  the  present  chapter  experiments 
will  be  reported  in  which  the  method  was  followed  with  three  ob- 
servers. The  results  of  Cattell  and  Fullerton,^  who  found  the  per- 
ception and  reproduction  of  extent  to  be  more  accurate  than  that 

""Small  Differences,"  pp.  103-llG. 


42  THE   INACCURACY    OF    MOVEMENT 

of  time  have  been  quoted  as  an  illustration  of  the  third  method. 
But  certain  disadvantages  in  the  apparatus  used  in  these  observa- 
tions seem  to  make  further  experiments  desirable.  In  the  experi- 
ments reported  by  these  authors  the  duration  of  the  movement  was 
not  completely  under  the  control  of  the  observer.  His  task  was  to 
reproduce,  by  a  movement  of  50  cm.,  the  time  of  a  previous  move- 
ment of  the  same  extent.  It  was  not  a  question  of  stopping  a  con- 
trolled movement  at  the  expiration  of  a  given  period,  but  of  reaching 
a  certain  fixed  point  at  such  a  time.  If  the  speed  was  miscalculated 
no  correction  could  be  made,  since,  if  the  distant  point  were  not  yet 
reached  at  the  proper  time  it  was  necessary  to  continue  the  move- 
ment beyond  the  time  felt  to  be  sufficient,  while,  if  the  point  hap- 
pened to  be  passed  too  soon,  the  record  was  already  made.  Under 
these  conditions  it  would  seem  that  perception  of  speed  rather  than 
perception  of  duration  was  under  investigation.  Moreover  these 
writers  report  data  for  only  ^,  ^  and  1  second.  With  the  duration 
more  perfectly  under  the  control  of  the  observer  the  perception  and 
reproduction  of  time  might  conceivably  be  found  to  be  more  accurate 
than  under  the  conditions  just  described.  With  the  present  appa- 
ratus such  conditions  are  easily  fulfilled.  As  the  car  moves  along 
the  track  the  duration  is  recorded  accurately  and  graphically  at 
every  point  in  the  progress  of  the  movement.  Variations  and  errors 
of  speed  need  not  interfere  with  the  execution  of  duration,  and  the 
recording  of  the  time  is  quite  independent  of  the  extent  passed 
over.  With  these  favorable  conditions  experiments  on  the  perception 
and  reproduction  of  duration  were  performed  on  two  subjects  and 
these  also  will  be  reported  in  the  present  chapter.  In  securing  the 
results  to  be  given  later  we  are  thus  applying  the  second  and  third 
methods  indicated  by  AVoodworth. 

On  the  basis  of  factor  explicitly  studied  and  method  followed  the 
experiments  may  be  divided  into  five  groups. 

1.  Determination  of  the  accuracy  of  perception  and  of  repro- 
duction of  extent.  In  these  experiments  four  observers  were  used. 
On  three,  W.,  H.  and  Bt.,  the  magnitudes  ranged  from  100  mm.  to 
400  mm.  This  total  range  was  broken  up  into  six  sections,  viz., 
100-150,  150-200,  200-250,  etc.,  and  75  trials  within  each  section 
were  made.  A  trial  consisted  in  (a)  the  execution  of  a  standard 
movement  the  magnitude  of  which  was  controlled  by  the  signal  from 
the  sound  hammer;  (6)  the  attempt,  at  the  word  of  the  operator,  to 
reproduce  the  extent  of  this  standard;  (c)  after  having  completed 
the  reproduction,  a  guess,  indicated  by  the  word  "more"  or  *'less," 
as  to  the  direction  in  which  the  error  probably  lay.     With  these 


RELATION    BETWEEN   EXTENT    AND    DURATION  43 

three  subjects  the  continuous  method  was  used,  the  terminal  point 
of  the  standard  serving  as  the  starting  point  of  the  reproduction. 
On  subject  L.  the  successive  method  was  employed,  the  initial  points 
of  the  two  movements  being  the  same.  A  wider  range  of  magnitudes 
was  thus  made  possible.  The  movements  used  varied  between 
150  mm.  and  650  mm.,  and  the  total  range  has  been  divided  into  five 
sections,  viz.,  150-250,  250-350,  etc.,  75  trials  being  made  within 
each  section.  In  the  calculation  of  error  the  separate  magnitudes 
were  collected  under  the  heading  of  the  section  within  the  limits  of 
which  the  standards  fell  and  the  per  cent,  error  calculated  for  each 
movement.  These  errors  were  then  averaged  to  secure  the  average 
per  cent,  error  for  the  group,  and  this  error  was  analyzed  into  con- 
stant and  variable  errors.  By  this  method  it  has  been  possible  to 
avoid  the  distracting  and  complicating  features  involved  in  earlier 
methods  of  controlling  the  magnitude  of  the  standard  movement. 
There  is  no  illusion  of  impact  and  yet  the  extent  is  completely  under 
the  control  of  the  operator.  At  a  comfortable  rate  of  movement  the 
reaction  time  in  stopping  the  movement  at  the  signal  is  exceedingly 
short.  An  important  advantage  lies  in  the  fact  that  however  delayed 
the  reaction  may  be  the  space  passed  over  in  its  execution  is  included, 
both  introspectively  and  objectively,  in  the  standard  extent  and  no 
allowance  need  be  made  for  it.  Not  only  is  the  illusion  of  impact 
absent  but  the  errors  arising  when  the  standards  are  free  movements 
determined  in  their  extent  by  the  observer  himself  are  not  present.® 

2.  Determination  of  the  accuracy  of  perception  and  reproduction 
of  duration.  These  experiments  were  made  on  three  subjects,  W., 
Bt.  and  H.  The  method  followed  was  precisely  that  of  Ex.  1,  except 
that  the  observer  tried  to  reproduce  the  duration  of  the  standard 
movement  instead  of  its  extent.  In  these  movements  the  observer 
endeavored  to  move  at  an  approximately  constant  speed,  and  this 
fact  enabled  the  operator  to  vary  the  standard  duration  in  the  same 
way  in  which  he  varied  the  extent  in  the  other  experiments,  by 
changing  the  position  of  the  slide,  the  contact  of  which  with  the 
prong  projecting  from  the  car  completed  the  sound  hammer  circuit 
and  thus  gave  the  signal  for  stopping  the  movement.  Having  ex- 
ecuted the  standard  movement,  the  observer,  at  the  command  of  the 
operator,  went  on  to  reproduce  its  duration  by  the  continuous  method. 
The  total  range  of  durations  used  was  between  1  sec.  and  3i  sec, 
and  has  been  divided,  for  purposes  of  calculation,  into  five  sections, 
viz..  1-1^,  1^-2,  etc.  The  calculation  of  error  was  performed  as  in 
the  case  of  extent:  the  per  cent,  error  of  each  trial  witliin  a  group 

•  See  Chapt.  II. 


44  THE   INACCURACY    OF    MOVEAIEXT 

being  averaged  to  secure  the  average  error  for  that  section,  and  this 
error  analyzed  into  constant  and  variable  errors.  Within  the  limits 
of  each  section  75  trials  were  made.  In  each  case,  as  in  the  experi- 
ments on  extent,  the  observer,  after  his  attempt  at  reproduction, 
guessed  as  to  the  probable  direction  of  his  error.  During  the  course 
of  the  experiment  frequent  intervals  occurred  which  were  below  or 
beyond  the  range  of  durations  chosen.  These  were  not  included  in 
the  table. 

These  two  experiments  are  calculated  to  bring  us  one  step  nearer 
our  conclusion.  If  we  find  that  the  error  of  perception  and  repro- 
duction for  time  is  greater  than  that  for  extent,  as  suggested  by 
Cattell  and  Fullerton,  we  may  be  justified  in  concluding  that  extent 
is  not  .judged  in  terms  of  time.  If  the  error  for  time  is  less  than  or 
equal  to  that  for  extent,  we  may  still  be  in  some  doubt. 

3.  Incidental  observation  of  the  relation  between  the  durations  in 
the  experiments  in  which  the  observer  tried,  in  his  most  natural  way, 
to  reproduce  the  extent.  Since  the  instrument  records  graphically 
not  only  the  extent  but  the  duration  there  is  no  difficulty  in  securing 
such  a  correlation.  The  observer  devotes  his  attention  to  the  extent 
of  his  movements.  The  observer  having  made  his  reproduction  and 
guessed  as  to  the  direction  of  his  error,  we  can  determine  two  facts 
concerning  the  process:  (a-)  whether  the  times  or  the  extent  of  the 
two  movements  agree  more  closely,  (&)  whether  or  not  the  subse- 
quent introspective  impression  indicated  by  the  judgment  of  "more" 
or  "less"  agrees  more  often  with  the  objective  relation  of  the  extents 
or  with  that  of  the  times. 

Further,  the  agreement  of  the  durations  secured  in  this  way  can 
be  compared: 

(a)  With  the  accuracy  of  the  reproduction  of  extent.  If  the 
times  are  perceived  an'd  reproduced  less  accurately  than  the  extents 
we  shall  not  be  justified  in  supposing  the  perception  of  time  to  be  the 
more  fundamental  of  the  two.  On  the  other  hand,  if  the  times  agree 
more  closely  than  the  extents  we  may  be  justified  in  further  consid- 
eration of  the  theory. 

(6)  With  the  accuracy  of  the  perception  and  reproduction  of 
time  intervals  when  such  performance  is  the  explicit  and  deliberate 
attempt  of  the  observer.  If  the  agreement  of  the  records  incident- 
ally secured  is  less  complete  and  uniform  than  in  the  ease  of  those 
explicitly  performed,  we  may  infer  that  the  judgments  of  extent 
were  not  made  in  terms  of  duration.  If  there  is  no  considerable 
deviation  in  the  results  secured  by  the  two  different  methods,  the 
theory  of  the  more  primitive  character  of  the  judgment  of  time,  as 
proposed  by  Loeb,  Kramer  and  Moskiewicz  and  Jaensch,  while  not 
demonstrated,  is  at  least  made  exceedingly  plausible. 


RELATION   BETWEEN   EXTENT   AND    DURATION  45 

4,  Incidental  observation  of  the  relations  of  tlie  extents  in  tlie 
experiments  in  which  the  observer  sought  to  reproduce  the  times. 
This  procedure  is  rendered  easy  by  the  same  features  of  the  appa- 
ratus that  make  the  preceding  observations  possible.  In  the  ob- 
server's attempts  to  reproduce  durations  we  have  the  extents  also 
recorded,  both  of  the  standard  and  of  the  reproduction,  (a)  If  we 
find  the  extents  to  disagree  more  than  the  durations  we  can  draw  no 
conclusion  at  all  except  that  the  perception  and  reproduction  of  the 
time  is  clearly  not  a  function  of  the  sense  of  extent  of  movement. 
(&)  But  if  we  find  the  extents  to  agree  equally  with  or  more  closely 
than  the  times,  it  is  possible  that  in  reproducing  time  one  seeks  to 
make  equal  extents  at  the  same  speed,  and  that  there  is  some  direct 
sense  for  speed  aside  from  the  conscious  relation  of  extent  and 
duration. 

5.  The  experiments  constituting  the  fifth  group  were  suggested 
by  the  procedure  of  Cattell  and  Fullerton  in  their  analysis  of  the 
total  error  into  error  of  perception  and  error  of  execution.  The 
objective  measurements  may  be  supposed  to  reveal  the  basis  of  the 
perception  involved  in  the  total  performance,  consisting  of  the  esti- 
mation of  the  standard  and  the  attempt  at  reproduction.  The  guesses 
as  to  the  probable  direction  of  the  error  we  may  expect  to  give  certain 
additional  information  on  the  same  point.  Of  course  the  reproduc- 
tion is  always  intended  to  be  equal  to  the  standard,  and  at  the  final 
moment  the  observer  feels  it  to  be  so.  Otherwise  he  would  correct 
it,  if  it  fell,  short,  by  prolonging  it.  Or  if  the  second  movement  hap- 
pened to  ''get  away"  from  him  and  this  error  was  recognized,  the 
consciousness  of  failure  would  result  in  a  judgment  of  "more." 
A  priori,  then,  one  might  be  led  to  expect  all  guesses  to  be  "more." 
As  a  matter  of  fact  we  get  guesses  of  both  ' '  more ' '  and  ' '  less. ' '  If 
they  turn  out  to  be  approximately  equal  in  number,  no  matter  what 
the  actual  error,  we  may  treat  them  as  merely  chance  guesses.  But 
if  one  type  considerably  exceeds  the  other  we  may  suppose  that  its 
direction  was  determined  by  an  actual  retrospective  difference  in 
either  the  extents  or  the  durations.  Thus,  if  we  find  guesses  of 
"more"  in  excess  and  on  consulting  the  objective  relations  of  the 
movements  we  find  a  tendency  to  a  positive  constant  error  in  the 
times  while  the  errors  of  the  extents  are  indifferently  distributed  or 
are  negative,  we  would  not  be  unjustified  in  assuming  that  the  direc- 
tion of  the  guesses  was  determined  hy  the  perception  of  time  rather 
than  by  that  of  extent.  Further  inference  would  depend  on  the 
nature  of  the  task  which  the  observer  was  explicitly  trying  to  accom- 
plish in  the  trials  concerned. 

Certain  other  points  descriptive  of  the  experiment  as  a  whole 


46 


TEE   INACCURACY    OF    MOVEMENT 


may  now  be  indicated.  In  all  trials  visual  criteria  were  eliminated, 
either  by  having  the  observer  work  with  closed  eyes  or  by  allowing 
him  to  wear  a  blind  mask.  In  the  beginning  of  the  experiment  the 
ears  were  plugged  in  order  to  exclude  the  secondary  criteria  afforded 
by  the  noise  of  the  apparatus  or  by  the  sound  of  the  vibrating  reed 
interrupter  which  controlled  the  magnet  of  the  time  marker.  But 
very  early  in  the  experiment  improvements  in  the  running  gear  of 
the  car  made  the  operation  of  this  apparatus  noiseless,  and  at  the 
same  time  the  interrupter  was  muffled  by  the  use  of  boxing  and  pad- 
ding. This  was  probably  an  unnecessary  precaution,  however,  for 
the  vibrations  at  the  rate  of  10  per  second  can  scarcely  serve  as 
criteria  for  duration. 

TABLE    XI 


Reproduction  of  Extent.     First  Column,  Deliberate. 
Column,  Incidental 
Observer  W. 


Second 


"3 

o 

mm. 

mm. 

mm. 

mm. 

mm 

mm. 

Average 

a 

M 

s 

« 

100-150 

150-200 

200-250 

250-300 

300-350 

350-400 

and  Trials 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

A.E. 

8            12 

12       18 

14        15 

9        18 

13 

13 

16        19 

12            16 

2 

C.E. 

-1     +     1 

+  9  +  5 

+16  —10 

0  —11 

—  1  - 

-10  —12  —19 

—     2     —     7 

V.E. 

8          11 

10      19 

14      13 

9       15 

IS 

12 

11          7 

11           IS 

Trials 

15          25 

15         3 

15      13 

15       22 

15 

15 

15        7 

90          85 

A.E. 

15           11 

14      10 

23      14 

18        5 

19 

9 

12      14 

17           11 

5 

C.E. 

+  1     +     6 

+  5  +  5 

+23  —  2 

+  5  +  1 

—  4  - 

-  7 

+  1  —14 

+     5    —     2 

V.E 

15          10 

U         9 

16      13 

17        7 

18 

6\     11        7 

15            9 

Trials 

15           19 

15      10 

15      15 

15      14 

15 

16 

15        8 

90          82 

A.E. 

13          35 

20      19 

22      23 

13      12 

12 

13 

17      20 

16          20 

10 

C.E. 

—  2+32 

+10  +10 

+13  +13 

+  5  +  2 

—  1  - 

-  7 

—15  —20 

-1-2     +     4 

V.E. 

12          22 

19      18 

20      22 

11      11 

12 

10 

10        6 

14          15 

Trials 

15           15 

15      25 

15       13 

15      15 

15 

17 

15      11 

90          96 

A.E. 

20           19 

10      12 

15       16 

15      17 

16 

11 

12      12 

15          16 

15 

C.E. 

+12     +  11 

+  4  +  1 

+  7  +  4 

+  34-6 

—  2  - 

-  1 

—  8  —12 

+     3     +     2 

V.E. 

19          18 

10      11 

14      14 

11      14 

16 

11 

11        5 

14          12 

Trials 

15           21 

15       17 

15      19 

15       14 

15 

11 

15        4 

90          86 

A.E. 

26           18 

20      14 

16      21 

23      18 

25 

17 

47      33 

28          20 

30 

C.E. 

—25     +     2 

—17  —  4 

—26  —14 

—23  —12 

—25  - 

-12 

—47  —33!—  27    —  12 

V.E. 

14         19 

17      IS 

9      14 

7       17 

10 

14 

4       8 

10        14 

Trials 

15           20 

15       17 

15      18 

15       18 

15 

13 

15         2 

90          88 

A.E. 

16          19 

15       15 

20      18 

16       14 

17 

13 

21      20 

18          17 

Av. 

C.E. 

—  3+10 

+  2  +  3 

+  7  —  2;—  2  —  4 

—  7  - 

-  7 

—16  —20 

6            8 

V.E. 

13          16 

U      14 

15       15.     11       13 

14 

11 

9        7 

13          IS 

Trials 

75         100 

75      72 

75      781     75      83 

lb 

72 

75       32 

450        437 

In  order  to  secure  information  concerning  the  influence,  on  the 
accuracy  of  reproduction,  of  the  time  interval  elapsing  between  the 
standard  and  the  attempt  to  repeat  it,  five  different  intervals  were 


RELATION    BETWEEN    EXTENT    AND    DURATION 


47 


used  throughout  all  the  experiments,  15  trials  for  each  section,  both 
for  time  and  for  extent,  being  made  with  intervals  of  2  sec,  15  with 
intervals  of  5  sec,  and  similarly  with  intervals  of  10  sec,  15  sec 
and  30  sec,  these  constituting,  for  each  section,  the  75  trials  men- 
tioned above.  The  results  on  the  influence  of  the  time  interval  will 
be  brought  together  in  Chapter  VI. 


TABLE    XII 
Reproduction  of  Extent.     First  Column,  Deliberate. 
Column,  Incidental 
Observer  E. 


Second 


O 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

Average 

a 

100-150 

150-200 

200-250 

250-300 

300-350 

350-400 

and  Trials 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

A.E. 

25        25 

19       12 

19 

16        15 

13       12 

10         9 

17        15 

2 

C.E. 

+25  +25 

+19  +  9 

+19 

+13  +  5 

+10  —  5 

+  8  —  6 

+16   +16 

V.E. 

U      13 

10        9 

9 

10     14 

11      11 

10        7 

11        11 

Trials 

15      12 

15        9 

15 

15      11 

15      14 

15      23 

90      69 

A.E. 

33      21 

20      18 

25      24 

23      15 

10      11 

11      10 

20      17 

5 

C.E. 

+33  +11 

+20  +15 

+  22  +10 

+23  +15 

+  7  +  4 

+  2  +  1 

+18  +  9 

V.E. 

14      U 

10      13 

13      22 

11        8 

8      10 

11       10 

11       15 

Trials 

15      15 

15      11 

15      11 

15       16 

15      18 

15      14 

90      85 

A.E. 

38      15 

22      34 

22      22 

29      17 

15      14 

9      11 

23      19 

10 

C.E. 

+38  +10 

+22  +30 

+22  +12 

+29  +13 

+14  +14+  6  —  7 

+22  4-11 

V.E. 

11        9 

14     20 

9      17 

9      10 

8      m      7      10 

10      15 

Trials 

15        4 

15        5 

15        9 

15      23 

15      24 

15      20 

90      85 

A.E. 

25 

28      20 

27      15 

24      13 

16      12 

20      12 

23      14 

15 

C.E. 

+25 

+25  +19 

+27  +11 

4  24  +  41+13  —  9 

+20  —12+22  +  3 

V.E. 

17 

15        9 

12      10 

9      14 

12      10 

7        7;     12      10 

Trials 

15 

15      11 

15       23 

15       15 

15      13 

15      11 

90      73 

A.E. 

18      12 

30        5 

21      12 

29      11 

21      10 

9        7 

21      10 

30 

C.E. 

+  7-7+28  +  1 

+21  —  1 

+29  +10;+16  +  3 

+  4-1 

+18  +  1 

V.E. 

16        8      19         5 

18      12 

17        8\     14      10 

9        7 

16        8 

Trials 

15        5j     15        3 

15      13 

15       21 !     15       26 

t 

15      16 

90      84 

A.E. 

28      18 

24      18 

23      18 

24      14 

15      12 

12      10 

21       15 

Av. 

C.E. 

+26  +10 

+23  +14 

+22  +  8 

424  +  9 

+  12  +  7 

+  8  —  5;     19        9 

V.E. 

U      16 

14      11 

12      15 

11      11 

11      11 

9        <?!     12      12 

Trials 

75      36!     75      39 

75      56 

75      86  i     75      95 

75      84 1  450    396 

So  far  as  possible  the  experiments  were  performed  in  an  order 
which  would  distribute  the  results  of  practise.  All  the  subjects  had 
made  a  great  many  preliminary  trials  before  the  records  presented 
in  the  present  chapter  were  taken.  In  general  but  one  or  two  time 
intervals  were  used  at  a  single  sitting,  and  the  various  magnitudes 
were  taken  in  a  chance  order,  except  toward  the  end  of  the  experi- 
ment, when  it  became  necessary  to  give  definitely  chosen  magnitudes 
in  order  to  secure  the  requisite  number  of  trials  for  each  section  of 
the  total  range. 


48 


THE   INACCURACY    OF    MOVEMENT 


The  results  for  each  observer,  for  both  extent  and  duration,  are 
shown  in  full  in  Tables  XI.  to  XVII,  The  records  on  separate  ac- 
curacy are  given  in  each  table  along  with  the  errors  for  the  same 
factor,  for  W.,  H.  and  Bt.  when  the  observer's  attention  is  fixed  on 
the  reproduction  of  the  other  factor.  Thus  in  Table  XI.  are  given 
the  A.E.,  C.E.  and  V.E.  for  observer  "W.,  for  the  perception  and 
reproduction  of  extents— in  the  first   column   under   each  section 

TABLE    XIII 

Reproduction  of  Extent.     First  Column,  Deliberate.     Second 

Column,  Incidental 

Observer  Bt. 


"3 

o 

mm. 

mm. 

mm. 

mm. 

mm.               mm. 

Average 

5 

a 

1 

100-150 

150-200 

200-250 

250-300 

300-350           350-400 

and  Trials 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

A.E. 

25       31 

17       23 

22        9 

16       26 

12        20 

22       13 

19       20 

2 

C.E. 

+23  +30 

+10  +19 

+  8  —  3—2  —10 

—  5  —20 

—21  — 13i+  2  +  1 

V.E. 

U      16 

17      18 

22      13\     16      23 

12        6 

9        9 

15      14 

Trials 

12       12 

11      14 

10      10     10      11 

10        6 

10       10 

63      63 

A.E. 

26      26 

27      30 

8      16i     16      13 

19      28 

27      17 

21       22 

5 

C.E. 

+23  +22 

+25  +27 

+  6  — 16'+13  +  3 

—17  —16 

—27  —17 

+  4        0 

V.E. 

23      19 

21      19 

6        9\     15      12 

12      15 

11        9 

15      14 

Trials 

11      16 

10      10 

10        6j     10        6 

13        5 

10      11 

63      53 

A.E. 

58      41 

35      14 

32      16l     10      17 

14      21 

23 

29      22 

10 

C.E. 

+51  +37 

+31  +10 

+32  +  9 

—  4  —16 

—10  —20 

—23 

+13  +  4 

V.E. 

38      26 

21       10 

17      15 

13        7 

IS        9 

10 

19      13 

Trials 

11       18 

10        6 

10      11 

14        8 

13      11 

10 

68      54 

A.E. 

87      45 

56      27 

28      16 

15      15 

13      22 

25      26 

37      25 

15 

C.E. 

+87  +41 

+56  +  4 

+26  —  2+8  —  9 

—  4  —11 

—25  —26 

+25  —  1 

V.E. 

S2      35 

29       26 

17      16     13        8 

14      18 

12        6 

20      18 

Trials 

10      10 

10      11 

10        4      10      15 

9        8 

10      10 

59      58 

A.E. 

73      27 

50      37 

30      18!     17      16 

13      21 

30      32 

36      25 

30 

C.E. 

+73  +21 

+49  +37 

+27  +  7 

+  9  +16 

-  1  +7 

—30  —32 

+21  +  9 

V.E. 

42      25 

40      26 

27      17 

15      10 

13      21 

7        7 

26      18 

Trials 

5      10 

5        6 

5        8 

5        6 

6        8 

8      12 

33      50 

A.E. 

54      34 

37      26 

24      15 

15      17 

14      22 

25      22 

28      23 

Av. 

C.E. 

+51  +30 

+34  +14 

+20  —  1+5  —  3 

—  7  — 12|— 25  — 22j     24      15 

V.E. 

29      24 

26      20 

18      14,     14      12 

13      14     10        8     18      15 

Trials 

48      66 

46       47 

45      38     49      46 

1 

51      38     48      43    287    264 

when  the  attempt  is  to  reproduce  extent,  in  the  adjacent  column 
when  the  attempt  is  to  reproduce  the  durations,  the  extent  being 
recorded  incidentally.  In  the  case  of  observer  L.  only  trials  for  the 
reproduction  of  extent  were  made,  and  the  table  gives,  alongside 
these  errors,  the  corresponding  errors  for  the  durations  of  the  same 
movements.  In  all  the  tables  the  records  are  grouped  under  their 
appropriate  sections,  and  the  results  for  the  different  time  intervals 
are  indicated  separately.     At  the  foot  of  each  table  the  results  for  the 


RELATION    BETWEEN    EXTENT   AND    DURATION 


49 


particular  sections  for  all  five  time  intervals  are  averaged,  while  on 
the  right  of  each  table  are  brought  together  the  results  of  each  sec- 
tion for  the  particular  time  intervals.  Reading  across  at  the  foot 
of  the  table  from  left  to  right  we  have  given  the  influence  of  the 
magnitude  on  the  amount  of  the  error,  while  reading  down  the 


TABLE    XIV 
Reproduction  of  Duration.    First  Column,  Deliberate. 
Column,  Incidental 
Observer  W. 


Second 


"3 

>• 

U 
O 

1-1.5  sec 

1.5-2 

sec. 

2-2.5 

sec. 

2.5-3 

sec. 

3-3.5 

sec. 

* 

3.5-4 

1-3  5  sec. 
Average 

a 

w 

sec. 

and  Trials 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per 
Cent. 

Per  Cent. 

A.E. 

8       22 

10 

15 

11 

16 

11 

18 

11 

28 

48 

10       20 

o 

C.E. 

—  1  +14 

+  1 

+  4 

0 

—  1 

—  6 

—  4 

—  7 

—28 

-48 

—  2  —  3 

£i 

V.E. 

8      21 

10 

U 

14 

16 

10 

16 

9 

4 

17 

10      14 

Trials 

15       24 

15 

18 

15 

28 

15 

13 

15 

6 

8 

75      89 

A.E. 

15       34 

18 

22 

13 

19 

8 

19 

8 

27 

22 

13      24 

5 

C.E. 

+12  +23 

+  3 

+11 

+  2 

—  7 

—  0.2 

—  9 

—  4 

—24 

+  7 

+  3-1 

V.E. 

10      28 

18 

18 

17 

18 

8 

17 

7 

14 

22 

12       19 

Trials 

15      18 

15 

12 

15 

24 

15 

23 

15 

11 

9 

75      88 

A.E. 

26      35 

24 

19 

12 

21 

8 

20 

7 

16 

20 

16      22 

10 

C.E. 

+26  +29 

+24 

—  1 

+  4 

+15 

+  2 

+  5 

+  2 

+  2 

—14 

+12  +10 

V.E. 

11      29 

11 

19 

12 

20 

7 

19 

9 

16 

16 

10      21 

Trials 

15        8 

15 

20 

15 

15 

15 

18 

15 

15 

13 

75      76 

A.E. 

27      29 

13 

24 

10 

36 

11 

22 

12 

18 

26 

15      26 

15 

C.E. 

+23  +20 

+  9 

+17 

+  4  +21 

+  4 

—22 

+  9 

—  1|— 21 

+10  +  7 

V.E. 

17      SO 

12 

19 

9 

35 

12 

18 

10 

18i     17 

12      24 

Trials 

15        8 

15 

8 

15 

11 

15 

5 

15 

17 

18 

75      49 

A.E. 

18      29 

13 

25 

8 

18 

7 

17 

10 

29 

19 

11      24 

30 

C.E. 

+  7  +  8 

+  0.: 

+13 

-1 

+12 

+  7 

+  5 

+  3 

+13|—  5 

+  4  +10 

V.E. 

16      26 

13 

22 

8 

17 

5 

12 

10 

27 

19 

10      21 

Trials 

15        3 

15 

10 

15 

10 

15 

3 

15 

15 

14 

75      41 

A.E. 

19      30 

16 

21 

11 

22 

9 

19 

10 

23 

27 

13      23 

Av. 

C.E. 

+14  +15 

+  8 

+  9 

+  2 

+  8 

+  1 

+  5 

+  0.4 

—14 

—15 

5      10 

V.E. 

15      27 

13 

18 

11 

21 

8 

16 

9 

16      18 

11      20 

i  Trials 

75      61 

75 

68 

75 

88i     75 

62 

lb 

64     62 

375    343 

*  Incidental. 


column  on  the  right  the  figures  indicate  the  influence  of  the  length- 
ening of  the  time  interval  on  the  accuracy  for  the  total  range  of  the 
standard  magnitudes.  The  figures  in  the  lower  right  hand  corner 
of  each  table  represent  the  average  errors  of  the  total  range  regard- 
less of  the  difference  in  time  interval.  We  are  now  ready  to  analyze 
the  results  according  to  the  principles  outlined  above. 

Taking  up  the  five  experiments  in  the  order  in  which  they  have 
been  described,  we  have  first  to  consider  those  on  the  accuracy  of 
perception  and  reproduction  of  extent  of  movement  when  the  stand- 


50 


THE   INACCURACY    OF    MOVEMENT 


ard  magnitudes  are  neither  free  movements  nor  movements  termina- 
ting in  impact,  but  controlled  movements,  the  magnitudes  of  which 
are  determined  by  their  arrest  on  the  part  of  the  subject  at  the  sound 
hammer  signal.  The  results  for  the  four  observers  are  to  be  found 
in  the  first  columns  under  each  section  in  Tables  XI,,  XII.,  XIII. 
and  XVII. 

TABLE    XV 

Repeoduction  of  Duration.     Fibst  Column,  Deubebate.     Second 

Column,  Incidental 

Observer  H. 


Int 

Error 

1-1.5 

sec. 

1.5-2 

sec. 

2-2.5 

sec. 

2.5-3 

sec. 

3-3.5  sec. 



Average 
and  Trials 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

A.E. 

23 

31 

15 

15 

9 

9 

7 

11 

7       12 

12         16 

2 

C.E. 

+23 

+31 

+11 

+15 

+  5 

+  2 

+  5 

+  2 

—  2  -12 

+  9+8 

V.E. 

6 

10 

12 

IS 

8 

9 

6 

16        6        7 

8       11 

Trials 

15 

18 

15 

34 

15 

26 

15 

9      15        3 

lb       90 

A.E. 

26 

22 

20 

15 

26 

12 

15 

9       14      10 

20       14 

5 

C.E. 

+26 

+22 

+19 

+14 

+10 

+  2 

+  15 

—  3+12  +  5 

+17     f  8 

V.E. 

9 

12 

10 

10 

11 

12 

8 

8      10        7 

9       10 

Trials 

15 

23 

15 

30 

15 

19 

15 

8 

15         7 

75       87 

A.E. 

14 

22 

26 

14 

29 

14 

23 

9 

22      17 

23       15 

10 

C.E. 

+  5 

+15 

+26 

+10 

+29 

+  8 

+23 

+  9 

+20  +  8 

+20   +10 

V.E. 

u 

19 

17 

13 

n 

12 

8 

12 

11       15 

13       14 

Trials 

15 

17 

15 

Tl 

15 

29 

15 

7 

15        5 

75       80 

A.E. 

19 

23 

23 

19 

11 

14 

8 

9 

31 

19       13 

15 

C.E. 

+13 

+18 

+23 

+16 

+  8 

+  8 

+  7 

—  4!+29 

+  16    +  9 

V.E. 

15 

18 

13 

15 

12 

12 

5 

9 

18 

12       12 

Trials 

15 

23 

15 

30 

15 

26 

15 

6 

15 

lb       85 

A.E. 

33 

16 

26 

17 

16 

16 

17 

14 

33 

25       13 

30 

C.E. 

+33 

+13 

+26 

+13 

+  10 

+13 

+  8 

—  2 

4-30 

+21    +  9 

V.E. 

23 

13 

11 

U 

U 

15 

15 

IS 

18 

16       14 

Trials 

15 

15 

15 

24 

15 

16 

15 

8 

15 

75       63 

A.E. 

23 

23 

22 

16 

18 

13 

14 

11 

22       13 

20       15 

Av. 

C.E. 

+20 

+20 

+21 

+14 

+12 

+  7 

+  12 

+  1 

+  16  +  0.3 

16         8 

V.E. 

IS 

14 

12 

13 

12 

12 

8 

12 

13      10 

12       12 

Trials 

lb 

96 

75 

140 

75 

116 

75 

38 

lb      15 

375     405 

For  W.  the  gross  average  per  cent,  error  for  the  several  sections 
varies  between  15  per  cent,  and  21  per  cent.,  with  an  average,  for  the 
total  range,  of  18  per  cent.,  and  increases  with  the  magnitudes  in 
rather  close  approximation  to  AA^eber's  law,  the  D.L.  being  between  ^ 
and  ^.  The  C.E.'s  are  not  large  in  the  final  average,  though  they 
range  from  — 16  per  cent,  to  -f  7  per  cent,  in  the  separate  sections, 
the  average  regardless  of  signs,^  for  the  total  range  being  6  per  cent. 

'  In  calculating  the  final  average  C.E.'s  signs  have  been  disregarded  in  all 
these  tables,  since  it  is  the  absolute  magnitude  rather  than  the  direction  of 
these  errors  which  is  significant  as  a  measure  of  accuracy. 


RELATION    BETWEEN   EXTENT   AND    DURATION 


51 


The  phenomenon  of  the  indifference  point  is  found  here,  but  is  seen 
to  be  due  to  the  constant  errors  in  the  cases  in  which  the  intervals 
were  rather  short,  no  positive  errors  occurring  in  the  individual 
averages  beyond  the  interval  of  15  sec.     With  these  short  intervals 


TABLE    XVI 
Reproduction  of  Duration.    First  Column,  Deliberate. 
Column,  Incidental 
Observer  Bt. 


Second 


Interval 

Error 

1-1.5  sec. 

1.5-2  sec. 

2-2.5  sec 

2.5-3  sec. 

3-3.5  sec. 

Averages 
and  Trials 

2 

A.E. 
C.E. 
V.E. 

Trials 

Per  Cent. 
31       23 

+29  +19 
17       19 
10      18 

Per  Cent. 
26       21 

+26  —  4 

9      21 

10       10 

Per  Cent. 

11        16 

0  —10 

11       16 

10       15 

Per  Cent. 
22       23 

-20  -20 
13      20 
10        5 

Per  Cent. 

20       14 

—20  —14 

9       10 

10       10 

Per  Cent. 
22       19 
+  3  —  6 

12       17 
50       58 

5 

A.E. 
C.E. 
V.E. 
Trials 

30      34 

+20  +25 
19      83 
10      13 

26      18 

+24  +  6 
16      22 
10       12 

15       24 
+  3  +11 

15  21 

16  20 

20  26 
+  2  —15 

21  24 
10      14 

10      30 

—  6  —30 

10        9 

10      11 

20      26 

+  9-1 

16      22 

66      70 

10 

A.E. 
C.E. 
V.E. 
Trials 

52      42 

+52  +40 

24      29 

12       18 

18       41 

+17  +18 
17      37 
10      16 

36      21 

+36  —  3 

7      20 

10      15 

16      21 

+11  —20 

15      18 

10        8 

18      32 
—  3  —32 

18        7 
10        5 

28      31 

+22  —  1 
16      22 
52       62 

15 

A.E. 
C.E. 
V.E. 
Trials 

51       37 

+51  +35 
30      22 
16      24 

32      17 

+27  +13 
17      13 
10      19 

18      24 

+12  -14 

13      20 

10      13 

13      21 

+  1  +  4 
IS      21 
10        4 

12      32 

—  9  —32 

10      15 

10        2 

25      26 

+16  +  1 

17      18 

56      62 

30 

A.E. 
C.E. 
V.E. 
Trials 

48      75 

+48  +75 

25      26 

10        7 

62      24 

+62  +24 
29       U 
10        9 

33      24 

+31  +11 
18      21 
50       66 

37      26 

+37  +  6 

12      24 

10      10 

15      18 

-3  —  6 

15      20 

10        7 

18      23 

—18  —  5 

6      33 

10        2 

36      34 

+25  +19 
17      21 
50      35 

Averages. 

A.E. 
C.E. 
V.E. 
Trials 

42      40 

+40  +39 
23      26 
58       80 

23      22 

+18  —  2 
12      20 
56      73 

17      22 
—  2  —11 

15      21 
50      38 

16       26 

—11  —23 

11       13 

50      30 

26      27 

20      17 

16      20 

264    287 

the  effect  on  judgment  of  the  total  range  of  magnitudes  has  time  to 
operate.  In  the  case  of  the  longer  intervals  the  separate  trials  are 
distributed  over  so  great  a  period  that  the  group  influence  is  not 
found  to  be  effective,  the  C.E.'s  being  all  negative.  The  final  vari- 
able errors  range  from  9  per  cent,  to  15  per  cent.,  averaging  13  per 
cent.,  and  increase  in  rough  accord  with  Weber's  law,  though  there 
is  indication,  in  the  fourth  and  sixth  sections,  of  a  tendency  toward 
a  slower  rate  of  increase. 

Turning  to  H.'s  table  we  find  remarkable  similarity  in  the  re- 
sults. The  A.E.'s  tend  to  be  slightly  larger  than  for  W.,  ranging 
from  12  per  cent,  to  28  per  cent.,  with  a  final  average  of  21  per  cent, 
as  over  against  18  per  cent,  for  W.     The  V.E.'s  are  identical  for 


52 


THE   ^ACCURACY    OF    MOVEMENT 


the  second,  fourth  and  sixth  sections,  and  in  no  section  is  the 
difference  more  than  3  per  cent.  The  final  average  V.E.  for  H.  is 
12  per  cent.,  as  over  against  13  per  cent,  for  W.  Only  in  the  case 
of  the  C.E.'s  is  there  great  deviation.  H.  has  no  negative  C.E.'s, 
hence  no  indifference  point  occurs.  It  may  be  noted  that  this  ob- 
server is  the  writer  and  that  he  had  already  performed  the  experi- 

TABLE    XVII 

Repeoduction  of  Extent.     First  Column,  Extents.     Second 

Column,  Duration 

Observer  L. 


Int. 

mm. 

mm. 

mm. 

mm 

mm 

Average 

150-250 

250- 

350 

350-450 

450-550 

550-650 

and  Trials 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

Per  Cent. 

A.E. 

16        26 

9 

19 

12 

17 

5 

14 

5 

13 

11       18 

2 

C.E. 

—12    +15 

—  6 

+10 

-10 

—  2 

+  0.3 

—  8 

—  2 

—13 

—  6  +  0.6 

V.E. 

11       20 

7 

15 

5 

17 

5 

10      4 

6 

6      U 

Trials 

15 

15 

15 

15 

15 

75 

A.E. 

13       16 

8 

13 

13 

14 

9 

13 

6 

15 

9      14] 

5 

C.E. 

-1+8 

—  6 

+  1 

—13 

—10 

—  8 

—12  —  3 

—  9 

—  6  —  4 

V.E. 

IS       17 

6 

13 

5 

10 

6 

7 

5 

10 

7       11 

Trials 

15 

15 

15 

15 

15 

75 

A.E. 

13       12 

12 

12 

12 

19 

12 

19 

9 

20 

12      17 

10 

C.E. 

-10   +  4 

—  9 

—11 

—11 

—13 

—10 

—IS 

—  9 

—20 

—10  —10 

V.E. 

7       U 

10 

10 

10 

14 

9 

9 

6 

6 

8      11 

Trials 

15 

15 

15 

15 

15 

75 

A.E. 

14       24 

11 

6 

6 

21 

5 

18 

3 

17 

8      20 

15 

C.E. 

—  5-8 

—  8 

—  3 

—  3 

—  9 

—  3 

— 14i—  0.5 

—14 

—  4  —11 

V.E. 

U       20 

9 

6 

6 

16 

5 

12       3 

14 

8      16 

Trials 

15 

15 

15 

15 

15 

75 

A.E. 

14       20 

7 

16 

16 

18 

9 

14 

8 

26 

12      18 

30 

C.E. 

-7+5 

+  1 

—13 

—13 

—  9 

—  9 

—14 

—  6 

—14 

—  7  —  7 

V.E. 

11        19 

7 

11 

11 

17 

5 

7 

5 

20 

7       15 

Trials 

15 

15 

15 

15 

15 

75 

A.E. 

14       20 

9 

12 

12 

18 

8 

16 

6 

18 

10      17 

Av. 

C.E. 

-7+5 

—  6 

—10 

—10 

—  9 

—  6 

—13—  4 

—14 

7        5 

V.E. 

11       18 

8 

7 

7 

15 

6 

9       5 

11 

7      IS 

Trials 

lb 

75 

75 

75 

lb 

375 

ments  of  Chapter  IV.  The  knowledge  of  the  usual  tendency  to 
constant  errors  in  such  trials  seems  to  have  operated,  though  quite 
unintentionally,  toward  correction.  The  C.E.'s  range  between 
-j-  8  per  cent,  and  +  26  per  cent.,  averaging  19  per  cent,  as  against 
6  per  cent,  for  W.  With  this  observer  all  the  errors  increase  con- 
siderably more  slowly  than  Weber's  law  would  require,  and  some- 
what more  rapidly  than  the  square  root  law  of  Cattell  and  Fuller- 
ton  suggests. 

The  errors  in  the  case  of  Bt.  are  still  larger.     The  A.E 's  ranging 
from  14  per  cent,  to  54  per  cent.,  averaging  28  per  cent.,  the  C.E's 


RELATION    BETWEEN    EXTENT    AND    DURATION  53 

ranging  through  —  25  per  cent,  to  +  51  per  cent.,  averaging  24  per 
cent,  and  the  V.E  's  varying  between  10  per  cent,  and  29  per  cent., 
and  increasing  much  more  slowly  than  the  square  root  law.  The 
final  average  V.E.  for  Bt.  is  18  per  cent.,  as  against  13  per  cent,  for 
W.  and  12  per  cent,  for  H.  The  phenomenon  of  the  I. P.  shows  itself 
after  all  intervals. 

The  results  secured  from  observer  L.,  by  the  successive  Inethod, 
appear  in  Table  XVII.,  in  the  first  column  under  each  section  and 
show  slightly  greater  accuracy  of  reproduction  than  was  found  in 
the  preceding  cases.  The  size  of  the  final  averages,  however,  is 
likely  to  be  misleading  here.  The  A.E.  and  V.E,  increase  with  the 
magnitude  at  a  rate  approximating  the  square  root  law,  and  since  the 
upper  limit  of  the  range  of  standard  magnitudes  is  much  higher 
here  than  in  the  case  of  W,  and  H,  the  final  average  errors  are  ex- 
pressed, in  per  cents,  by  smaller  figures.  But  if  we  inspect  the 
lower  part  of  the  range  which  is  common  to  all  the  tables,  the  errors 
are  found  to  be  only  slightly  less.  For  L.  the  A.E.'s  for  the  total 
range  vary  between  6  per  cent,  and  14  per  cent.,  averaging  10  per 
cent.,  the  C.E.'s  are  all  negative  and  range  from  — 4  per  cent,  to 
—  10  per  cent.,  averaging  7  per  cent.,  while  the  V.E.'s,  lying  between 
5  per  cent,  and  11  per  cent.,  average  7  per  cent.  The  absence  of  an 
indifference  point  is  to  be  explained  by  the  fact  that  no  effort  was 
made  to  produce  a  series  effect— that  is  to  say,  the  magnitudes  used 
at  a  single  sitting  or  taken  on  a  single  record  sheet  did  not  vary 
over  the  total  range  but  lay  within  a  few  adjacent  sections. 

The  results  of  the  second  group  of  experiments,  on  perception 
and  reproduction  of  duration,  are  indicated  in  Tables  XIV.-XVI. 
in  the  first  columns  under  each  section.  For  W.  the  A.E.'s  for 
the  separate  sections  range  from  9  per  cent,  to  19  per  cent.,  aver- 
aging 13  per  cent.,  and  increasing  with  the  magnitude  of  the 
standard  in  close  agreement  with  a  cube  root  law.  The  sectional 
C.E.'s  range  from  -f-  1  per  cent,  to  +  14  per  cent.,  averaging  5  per 
cent.  Of  considerable  interest  is  the  fact,  already  mentioned  in 
another  connection,  that  an  indifference  point  shows  itself  only 
when  the  time  intervals  are  so  short  as  to  allow  the  judgment  to  be 
influenced  by  the  group  effect.  The  variable  error  ranges  through 
8-15  per  cent,  averaging  11  per  cent,  and  increasing  with  the  mag- 
nitude with  an  approximation  to  a  cube  root  law.  In  the  table  for 
H,  the  A.E.'s  increase  according  to  Weber's  law,  ranging  between 
14  per  cent,  and  23  per  cent,  and  averaging  20  per  cent.  The  C.E.'s 
are  positive,  varying  from  12  per  cent,  to  21  per  cent,  with  an  aver- 
age at  16  per  cent.  No  indication  of  an  indifference  point  is  present 
except  after  the  2-sec.  interval.     The  V.E.  seems  to  follow  Weber's 


54  THE    INACCURACY    OF    MOVEMENT 

law,  being  remarkably  constant  in  terms  of  per  cent,  and  averaging 
12  per  cent,  for  the  total  range  as  over  against  11  per  cent,  in  the 
case  of  AV. 

In  the  case  of  Bt.  again,  all  errors  are  greater,  and  the  constant 
errors  change  their  sign  at  the  indifference  point  for  this  particular 
range  of  magnitudes— about  2.5  sec.  All  errors  increase  too  slowly 
for  even  a  square  root  law,  the  final  averages  being,  A.E.  26  per  cent., 
C.E.  20  per  cent.,  V.E.  16  per  cent. 

These  two  experiments  completed,  we  have  complied  with  the 
conditions  of  the  third  method  proposed  by  Woodworth.  We  now 
have  separate  accuracy  tests  for  extent  and  for  such  durations  as 
are  ordinarily  employed  in  the  execution  of  such  extents,  and  are 
in  position  to  compare  the  records.  Bringing  together  the  final 
averages  for  the  three  subjects  we  have  the  following. 


TABLE    XVIII' 

W. 

H. 

Bt. 

A.E.    C.E. 

V.E. 

A.E.         C.E.             V.E. 

A.E. 

C.E. 

V.E. 

Extent 

18     6±2 

13±.6 

21     I9±1.7     12±.6 

28 

24±3.8 

18±1.5 

Time 

13     5±1.3 

11±.7 

20     16±2        12±.9 

26 

17±2.8 

16±1.2 

If  these  averages  are  taken  at  their  face  value  the  results  are  just 
the  reverse  of  those  of  Fullerton  and  Cattell.  With  the  single  ex- 
ception of  H.'s  V.E.  all  the  actually  obtained  errors  are  less  for 
time  than  for  extent.  But  the  differences  in  the  case  of  the  V.E.'s 
of  W.  and  Bt.  are  exceedingly  small,  and  in  the  case  of  Bt.  quite 
within  the  limits  of  error  of  the  averages  compared.  The  same  is 
true  of  the  C.E.'s  of  W.  and  H.,  while  H.'s  V.E.'s  agree.  Positive 
inference  as  to  the  greater  accuracy  of  perception  and  reproduction 
of  time  would  be  insecure,  although  the  results  tend  on  the  whole, 
to  suggest  such  an  inference.  The  separate  accuracy  tests,  then, 
yield  little  information  as  to  the  probable  basis  of  the  judgment  of 
extent.  If  the  errors  in  the  case  of  extent  had  been  smaller  than 
those  for  time  there  would  have  been  reasonable  certainty  that  the 

*  In  Tables  XVIII.,  XIX.  and  XX.  the  reliability  of  the  average  V.E.  and 
C.E.  is  given  in  terms  of  mean  square  error.  The  measure  of  variability  was 
calculated  from  the  formula  (A.D.  X  1.25  )/V«',  in  which  A.D.  =  the  average 
deviation  of  separate  V.E.'s  of  Tables  XI.-XVI.  from  their  final  averages,  and 
n  =  the  number  of  determinations  of  the  V.E.  under  different  conditions  of 
magnitude  and  interval.  In  most  cases  this  number  was  30.  The  chances  are 
thus  about  2:1  (more  exactly,  68:32)  that  the  true  final  average  does  not  differ 
from  that  obtained  from  our  figures  by  more  than  this  mean  square  error.  Thus 
in  Table  XVIII.  the  chances  are  2:1  that  W.'s  V.E.  for  extent  lies  between  12.4 
and  13.6,  or  similarly  that  his  V.E.  for  time  is  not  less  than  10.3  or  greater 
than  11.7.  See  Thorndike,  "Mental  and  Social  Measurements,"  Science  Press, 
New  York,  1904,  pp.  59  and  139. 


RELATION    BETWEEN    EXTENT    AND    DURATION  55 

judgment  of  extent  was  not  made  on  the  basis  of  the  duration  of 
the  movement.  On  the  other  hand,  had  the  accuracy  for  time  been 
greater  than  that  for  extent,  there  would  have  been  reason  for  sup- 
posing the  temporal  judgment  to  be  the  more  fundamental.  Per- 
haps as  reasonable  a  conclusion  as  any  from  the  figures  as  they  stand 
would  be  that  the  judgments  of  the  time  and  the  extent  of  our 
movements  are  identical. 

This  can  be  decided  finally  only  by  the  methods  of  correlation 
next  to  be  considered.  Of  the  three  methods  proposed  by  Wood- 
worth  the  first  and  third  yield  results  somewhat  favorable  to  the 
hypothesis,  through  the  following  facts: 

(a)  Disturbance  of  the  time  element  has  been  found,  by  other 
investigators,  to  confuse  the  perception  of  extent. 

(6)  The  present  experiment  seems  to  suggest- the  possibility  of 
slightly  greater  accuracy  of  perception  and  reproduction  of  time, 
though  the  evidence  is  slight.  But  the  experiment  affords  positive 
evidence  that  the  accuracy  for  time  is  not  less  than  for  extent. 

"VVe  have  now  to  consider  the  agreement  of  the  durations  when 
the  observer  is  attending  to  the  extents,  in  the  cases  of  all  four  sub- 
jects. The  records  for  W.,  H.  and  Bt.  are  to  be  found  in  Tables 
XIV.-XVI.,  in  the  second  columns  under  each  section  heading, 
parallel  with  the  errors  when  the  durations  themselves  are  the  object 
of  attention.  For  W.  the  gross  errors,  ranging  from  19  per  cent, 
to  30  per  cent.,  average  23  per  cent.,  the  final  C.E.  is  10  per  cent, 
and  the  V.E.'s,  varying  between  16  per  cent,  and  27  per  cent.,  aver- 
age 20  per  cent.  For  H.  the  A.E.,  C.E.  and  V.E.  are  considerably 
lower,  averaging  15  per  cent.,  8  per  cent,  and  12  per  cent.  For  Bt. 
the  gross  errors  range  through  22  per  cent,  to  40  per  cent.,  averaging 
27  per  cent.,  the  final  C.E.  is  17  per  cent,  and  the  V.E.'s,  varying 
between  13  per  cent,  and  26  per  cent.,  average  20  per  cent.  The  re- 
sults for  L.  are  indicated  in  Table  XVII.,  parallel  with  his  records 
for  extent.  In  the  calculation  of  these  results  a  slightly  different 
method  Avas  used.  The  durations  did  not  range  widely,  since  there 
seemed  to  be  a  tendency  to  make  all  the  movements  in  a  time  be- 
tween the  limits  of  .8  and  1.5  sec.^  Consequently,  in  calculation  the 
durations  were  not  distributed  under  sections  but  the  actual  dura- 
tions employed  in  making  movements  of  a  given  extent  section 
were  compared  and  the  error  computed  for  the  durations  under 
each  extent  section.  In  the  two  columns  then  we  have  the  error  for 
extent  and  the  error  for  duration  for  the  same  movements.     The 

'  This  tendency  may  stand  in  some  relation  to  tlie  idea  of  a  most  comfort- 
able interval  advanced  by  Jaensch  in  the  case  of  movements,  and  by  others  in 
general  studies  of  time  sense. 


56  TEE    INACCURACY    OF    MOVEMENT 

A.E.  for  duration  is  17  per  cent.,  the  C.E.  5  per  cent  and  the  V.E. 
13  per  cent.  We  are  now  in  position  to  compare  the  accuracy  for 
extent  with  the  agreement  of  the  durations  incidentally  secured. 
We  may  bring  together  the  results  as  follows: 


TABLE    XIX 

W. 

H. 

Bt. 

L. 

A.E. 

C.E.          V.E. 

A.E. 

CE.            V.E.         A.E. 

C.E. 

V.E. 

A.E.      C.E.          V.E. 

Extent    18 

6±2      13±.6 

21 

19±1.7    12±.6       28 

24±3.8 

18±1.5 

10    7±   .8     7±.6 

Time       23 

10±1.8  20±.9 

1.5 

8it  .9    12±.9       27 

17±2.8 

20±1.3 

17    5±1.5  13±.9 

Two  features  of  this  table  seem  to  me  to  afford  basis  for  positive 
inference  of  considerable  reliability.  First,  if  we  take  the  V.E.'s 
alone,  we  get  results  decidedly  the  reverse  of  those  of  Table  XVIII. 
In  that  table  the  errors  for  extent  were  never  smaller  than  for  time. 
In  the  present  table  they  are  never  larger.  On  the  contrary,  the 
V.E.  for  time  is  greater  by  50  per  cent,  in  the  case  of  AY.,  by  100 
per  cent,  in  the  case  of  L.  With  Bt.  the  V.E.  for  time  is  greater, 
but  the  probable  error  is  larger  here  than  w^th  the  other  subjects. 
In  H.'s  case  the  V.E.'s  for  extent  and  time  under  all  conditions 
average  exactly  the  same  and  h'ave  about  the  same  probable  error. 
It  should  be  noted  that  H.  is  the  writer  and  that  in  all  the  observa- 
tions on  him  he  was  aware  of  the  procedure  and  purpose  of  the  experi- 
ment. This  fact  was  felt  introspectively  to  give  a  certain  prom- 
inence to  temporal  relations  even  in  reproductions  of  extent,  while 
in  reproductions  of  duration  attention  was  called  to  spatial  rela- 
tions more  than  would  be  the  case  with  a  naive  subject.  Bt.  also 
knew  something  of  the  purpose  of  the  experiment,  having  listened  to 
a  short  preliminary  report.  The  rather  close  agreement  in  the  case 
of  these  two  subjects,  in  contrast  with  the  striking  differences  in  the 
case  of  the  other  two,  is  probably  indicative  of  the  difference  in 
attitude  resulting  from  the  knowledge  of  the  experiment  and  the 
unnatural  prominence  given  to  the  incidental  factor  in  each  judg- 
ment. Comparing  Tables  XVIII.  and  XIX.  we  may  say,  with  con- 
siderable certainty,  that,  although  deliberate  times  fall  out  some- 
what more  accurately  than  extents,  incidental  times  are  subject  to 
greater  V.E.'s  than  their  corresponding  extents.  There  must,  there- 
fore, be  some  regulation  of  the  extent  independent  of  the  incidental 
regulation  of  duration. 

We  have  yet  to  observe  the  C.E.'s  of  Table  XIX.  In  the  case 
of  W.  the  C.E.  for  time  is  greater  than  that  for  extent,  agreeing  with 
the  relation  of  the  V.E.'s  and  confirming  the  results  of  the  preced- 
ing paragraph.  In  the  other  three  cases  the  C.E.'s  are  smaller  for 
time.     In  the  case  of  these  three  observers  the  C.E.'s  throughout 


RELATION    BETWEEN    EXTENT    AND    DURATION  57 

the  experiment  are  smaller  for  the  incidental  magnitudes  than  for 
the  deliberate  (for  extent,  see  Table  XX.).  With  these  three  sub- 
jects the  C.E.  seems  to  be  more  intimately  bound  up  with  the  proc- 
ess of  deliberate  reproduction,  or  of  attention  to  a  certain  magni- 
tude. When  extent  is  attended  to  it  is  subject  to  a  greater  C.E. 
than  when  its  reproduction  is  incidental  to  the  reproduction  of  a 
time  magnitude.  The  C.E  for  this  deliberately  reproduced  extent 
is,  moreover,  greater  than  that  of  the  time  magnitudes  incidentally 
employed.  Similarly  the  deliberate  reproduction  of  time  is  affected 
with  greater  C.E.  than  the  incidental  reproduction  of  either  time  or 
extent.  Although  this  relation  does  not  hold  for  subject  W.,  its 
prominence  in  the  results  of  H.,  Bt.  and  L.  seems  to  indicate  a 
certain  separation  between  the  magnitude  attended  to  and  the  other. 
This  separation  would  arg-ue  for  separate  processes  of  judgment  for 
the  two  magnitudes,  extent  and  time. 

We  have  yet  to  compare  our  incidental  measurements  of  dura- 
tion with  those  yielded  by  the  deliberate  attempt  to  reproduce  time, 
in  the  case  of  observers  W.,  H.  and  Bt.  These  records  are  to  be 
found  in  Table  XX.,  along  with  the  corresponding  records  for  extent. 

I  TABLE   XX 

W.  H.  Bt.  L. 
A.E.     C.E.  V.E.      A.E.       C.E.         V.E.       A.E.      C.E.           V.E.           A.E.     C.E.        V.E. 
Extent — 
deliberate  18     6±2  13±.6      21   19±1.7   12±.6      28  24±3.8  18±1.5      10  7±  .8     7±.6 
incidental   17     8=!zl.7  13±.8      15     9±1.3  12±.6      23   15±2.2  15±1.2 
Time- 
deliberate   13     5±1.3  11±.7      20   16±2      12±.9      26  20±3.5   16±1.2 
incidental  23   10±1.8  20±.9      15     8±  .9   12ih.6      27   17±2.8  20±1.3      17  5±1.5   13±.9 

In  the  earlier  description  of  this  experiment  the  criterion  for 
our  conclusion  M^as  stated  in  these  words:  "  If  there  is  no  consid- 
erable deviation  in  the  results  secured  by  the  two  methods  (deliber- 
ate and  incidental),  the  theory  of  the  more  primitive  chai^cter  of 
the  judg-ment  of  time  ...  is  at  least  made  exceedingly  plausible." 
But  "considerable  deviations"  are  present.  Only  in  the  case  of  H. 
is  there  approach  to  agreement,  the  V.E.'s  here  being  equal.  The 
significance  of  the  smaller  C.E.  for  incidental  time,  shown  here  m 
the  case  of  H.,  Bt.  and  L.,  has  already  been  discussed.  But  the 
V.E.'s  for  W.  and  Bt.  are  much  greater  for  incidental  than  for 
deliberate  time,  almost  twice  as  large  for  W.  and  a  fourth  again  as 
large  for  Bt.  If  duration  were  used  as  the  basis  of  the  judgment 
of  extent,  we  should  expect  as  great  accuracy  in  the  case  of  the 
incidental  times  as  in  the  case  of  the  deliberate.  Except  for  the 
observation  on  the  writer,  this  is  not  found. 


58  THE    INACCURACY    OF    MOVEMENT 

Summing  up  the  results  of  the  experiment  up  to  this  point,  we 
may  say  that  though  the  argument  is  not  overwhelming,  the  balance 
of  evidence  seems  to  show  that  while  deliberate  times  are  somewhat 
more  accurately  reproduced  than  deliberate  extents,  incidental  times 
show  an  error  greater  than  either,  and  this  fact,  along  with  the 
character  of  the  C.E.'s  points  to  separate  processes  of  judgment  for 
the  two  magnitudes.  There  is  at  least  no  justification  for  the 
attribution  of  more  fundamental  character  to  either  judgment. 

There  is  still  another  method  of  handling  the  data  afforded  by 
these  experiments  which  may  be  supposed  to  throw  some  light  on 
the  amount  of  interdependence  between  the  judgments  of  extent 
and  of  duration— the  method  of  correlation.  Ignoring  the  actual 
magnitude  of  error,  we  may  regard  each  particular  error  solely 
from  the  point  of  view  of  its  direction  and  correlate  the  errors  for 
extent,  in  the  case  of  a  standard  and  its  reproduction,  with  the 
incidental  error  or  difference  in  the  corresponding  durations.  Sim- 
ilar correlations  may  be  made  between  the  errors  for  time  (in  the 
attempt  to  reproduce  duration)  and  the  incidental  differences  of 
the  corresponding  extents.  Such  correlations  have  been  made,  for 
both  cases,  and  for  all  observers,  by  the  method  of  unlike  signs. 
Thus  each  error  in  the  case  of  reproduction  of  extent  was  classified 
as  4"  or  — J  ^^^  the  errors  of  the  incidental  times  classified  in  the 
same  way,  regardless  of  their  magnitude.  These  signs  were  then 
compared,  in  the  case  of  each  separate  trial,  for  each  magnitude 
and  the  per  cent,  of  unlike  signs  computed  for  each  observer.  The 
same  calculation  was  made  for  the  reproductions  of  duration.  From 
the  resulting  per  cent,  of  unlike  signs  we  are  able  to  get  the 
approximate  coefficients  of  correlation  given  in  Table  XXI. 

TABLE    XXI 

Giving  Per  Cent,  of  Unlike  Signs   {U)  and  Corresponding  Pearson 

Coefficients   (r=cos  nil)   of  Correlations  BET^yEEN  Errors 

OF  Extent  and  Errors  of  Duration 

Observer.  W.  H.  Bt.  L. 

Reproducing  extent    

Reproducing   time    


per  cent.  U 

43 

31 

21 

32 

r 

.22 

.56 

.79 

.54 

per  cent.  V 

40 

32 

26 

r 

..31 

.54 

.67 

We  may  discuss  the  two  groups  separately: 

(a)  Correlations  between  deliberate  extents  and  incidental  dura- 
tions. If  in  these  observations  the  judgment  of  extent  is  based  upon 
the  perception  of  duration,  we  should  expect  high  positive  correla- 
tion—that is,  the  direction  of  the  extent  errors  should  correspond 


RELATION    BETWEEN    EXTENT   AND    DURATION  59 

closely  to  the  direction  of  the  differences  in  time.  In  fact,  if  the 
speed  of  all  the  movements  was  equal  and  uniform  we  should  expect 
perfect  correlation,  and  a  reproduction  occupying  more  time  than 
its  standard  would  also  cover  more  space.  The  only  factor  tending 
to  reduce  the  positive  correlation  would  be  variation  in  speed.  If 
the  standard  and  reproduction  were  made  at  different  rates  and  the 
perception  of  duration  were  more  fundamental,  the  reproduction,  if 
slower,  would  be  shorter,  if  faster  it  would  be  longer,  than  the 
standard,  and  the  errors  for  extent  would  be  greater  than  for 
(incidental)  time.  We  have  found  just  the  reverse  to  be  true  (Table 
XIX.).  Consequently,  if  the  perception  of  duration  is  here  serving 
as  the  basis  of  judgment,  we  must  suppose  that  the  speed  is  prac- 
tically equal  and  uniform  in  the  case  of  standard  and  reproduction. 
In  which  case  very  high  positive  correlation  is  required.  A  chance 
relation  will  be  indicated  by  r  =  0  in  which  case  per  cent.  U  =  50. 
The  actually  obtained  correlations  are,  as  a  matter  of  fact,  positive 
and  rather  high  in  three  cases,  in  the  other  case  positive  though 
rather  low,  the  four  r's  being  .22,  .56,  .79  and  .54,  averaging  .53. 
As  far  as  these  figures  go  there  seems  to  be  a  pretty  strong  tendency 
for  errors  in  extent  to  correspond  to  errors  in  duration. 

(&)  Correlations  between  deliberate  durations  and  incidental  ex- 
tents.    There  are  two  conceivable  ways  of  approaching  these  data: 

(1)  Let  us  suppose  the  perception  of  time  to  be  fundamental  and 
the  perception  of  extent  derived.  Then  in  the  reproductions  of  dura- 
tions we  have  no  right  to  expect  close  correspondence  of  the  incidental 
extents  except  in  so  far  as  there  is,  on  the  part  of  the  observer,  an 
habitual  tendency  to  make  movements  agree  in  both  respects.  At 
any  rate,  we  should  expect  the  extent  errors  to  be  greater  than  those 
for  duration.  But  we  actually  do  find  almost  as  high  correlation  in 
this  case  as  in  the  preceding  section,  the  three  r's  being  .31,  .54  and 
.67,  averaging  .51,  as  against  .53  in  the  reproductions  of  extent. 
Moreover,  if  we  compare  the  accuracy  of  the  deliberately  reproduced 
durations  with  the  incidental  variations  of  the  extents  (Table  XIX.) 
we  find  the  V.E.'s  to  be  indistinguishable  and  the  C.E.'s  in  two  cases 
(H.  and  Bt.)  actually  smaller  for  extent,  while  for  W.  the  C.E.  for 
extent  is  slightly  larger  than  for  time,  though  the  probable  errors  of 
the  two  do  not  allow  them  to  be  at  all  sharply  distinguished. 

(2)  Let  us  suppose,  for  sake  of  comparison,  that  the  perception 
of  duration  is  based  on  that  of  extent.  We  should  thus  expect,  on 
the  same  argument  as  that  outlined  in  section  (a),  high  positive  cor- 
relation between  extent  and  time.  And,  as  already  pointed  out, 
we  get  a  coefficient  (.51)  practically  as  high  as  in  section  (a),  (.53). 
Following  out  the  argument  of  section  (a),  we  find  indications  of  a 
dependence  of  the  time  judgment  on  the  perception  of  extent. 


60 


THE   INACCURACY    OF    MOVEMENT 


The  method  of  correlation,  then,  affords  no  very  conclusive  evi- 
dence on  the  question  of  primitiveness.  All  the  coefficients  show  is 
that  there  is  a  considerable  positive  correlation  between  extent  and 
duration,  no  matter  which  factor  the  observer  is  deliberately  trying 
to  reproduce. 

The  result  of  the  observers '  guesses  as  to  the  probable  direction  of 
their  errors  have  yet  to  be  presented.  The  per  cent,  of  right  guesses 
for  all  the  different  cases  is  shown  in  Table  XXII.,  which  shows  the 
correspondence  of  the  guesses  for  both  factors  in  each  experiment. 


TABLE 

XXII 

Factor. 

w. 

H. 

Bt. 

L. 

Task. 

Per  Cent. 
Right. 

Per  Cent. 
Right. 

Per  Cent. 
Right. 

Per  Cent. 
Right. 

Times  to  be 
equal. 

Extents  to  be 
equal. 

Times. 
Extents. 

Extents. 
Times. 

46 
49 

59 
53 

52 
56 

54 

58 

61 

65 

64 
63 

60 

56 

The  observer  guessed  with  respect  to  the  deliberate  magnitude  only, 
but  the  table  gives  the  correspondence  of  these  +  or  —  guesses  with 
the  +  and  —  variations  of  both  the  deliberate  and  the  incidental 
magnitudes. 

"We  have  found  (Table  XIX.)  that  in  reproductions  of  extent, 
extent  falls  out  more  accurately  than  time.  Table  XXIII.  shows 
that  in  three  cases  out  of  four  the  guesses  agreed  more  closely  with 
the  actual  relations  of  the  extents  than  with  those  of  the  durations. 
There  is  here  a  suggestion  that  the  subsequent  guess,  and,  supposedly, 
the  initial  judgment,  were  made  on  the  basis  of  the  factor  explicitly 
attended  to  (extent).  However,  the  same  relation  holds  in  the  ex- 
periments on  reproduction  of  time.  Even  here  the  guesses  corre- 
spond more  closely  with  the  actual  relations  of  the  extents,  although 
we  saw  (Table  XX.)  that  there  is  no  clear  difference  in  accuracy  of 
reproduction.  The  percentages  of  right  cases  are  not  high,  as  50 
per  cent,  would  indicate  only  chance  relationship.  Moreover,  the 
reliability  of  a  statement  of  per  cent,  of  right  guesses  lying  within 
quite  a  wide  region  above  and  below  50  per  cent,  is  not  great.  The 
reliability  of  any  one  of  the  figures  in  Table  XXII.  may  be  calcu- 
lated from  the  formula  o-  =  \/pq/n,  in  which  p  =  proportion  of 
cases  in  which  the  event  occurs  (per  cent,  of  right  guesses),  and 
g' =  proportion  of  cases  in  which  the  event  does  not  occur  (per  cent, 
of  wrong  guesses).  In  all  these  cases  n,  the  total  number  of  guesses, 
is  about  400.     This  gives  a  probable  error  of  about  1.7  per  cent,  for 


RELATION    BETWEEN    EXTENT    AND    DURATION  61 

each  of  these  j5gures,  which  gives  a  low  reliability  to  the  differences 
actually  shown.  But  the  fact  that  in  six  out  of  the  seven  cases  the 
guesses  correspond  more  closely  to  the  actual  errors  of  the  extents 
than  to  those  of  the  times  is  unfavorable  to  the  hypothesis  that  it  is 
the  perception  of  time  on  which  the  judgment  of  extent  is  based. 
Another  argument  in  the  same  direction  is  the  fact  that  the  propor- 
tion of  right  guesses  in  experiments  on  the  reproduction  of  extent  is 
greater,  for  all  observers,  than  the  proportion  of  right  guesses  in 
the  experiments  on  reproduction  of  duration. 

These  considerations  seem  to  have  additional  significance  when 
taken  in  connection  with  the  comparison  of  the  accuracy  of  reproduc- 
tion for  deliberate  and  incidental  extents.  Extents  are  seen  to  agree 
as  closely  when  the  observers  are  reproducing  time  as  when  they  are 
attending  to  the  extents,  though  it  is  not  true  that  times  incidentally 
measured  are  as  accurately  reproduced  as  those  deliberately  made. 
Instead  of  finding  judgments  of  extent  dependent  on  the  perception 
of  time  we  find  indications  of  the  more  primitive  character  of  the 
judgment  of  extent.  At  least  the  same  argument  which  in  experi- 
ments 1  and  2  excluded  time  as  a  factor  of  the  judgment  of  extent 
now  leads  us  to  conceive  the  possible  importance  of  the  perception 
of  extent  in  the  process  of  reproducing  duration.  The  judgment,  it 
is  true,  may  not  be  expressed  in  spatial  terms — it  may  be,  on  the 
other  hand,  that  the  fundamental  perception  is  of  speed  or  rate  of 
movement,  and  that  the  agreement  of  the  extents  is  merely  incidental 
to  the  reproduction  of  the  speed.  Reproduction  of  speed  would  call 
for  nearly  equal  force  or  energy  of  contraction,  and  result  in  the 
production  of  a  movement  tending  to  agree  in  all  respects— speed, 
extent  and  duration.  That  movements  do  tend  to  agree  in  all  their 
attributes  and  that  observers  tend  not  so  much  to  reproduce  par- 
ticular characteristics  as  to  repeat  the  previous  performance  in  its 
entirety  we  have  already  seen  in  Chapter  II.  And  in  the  measure- 
ments of  speed  in  in  that  chapter,  for  just  such  movements  as  those 
used  in  the  present  experiment,  we  found  deviations  of  only  2  per 
cent,  average  in  movements  at  the  rate  of  100  mm.  per  second.  No 
such  per  cent,  accuracy  is  found  for  either  extent  or  time.  Com- 
parison of  the  agreement  of  the  incidentally  reproduced  extents  with 
that  of  the  deliberately  reproduced  durations  leads  to  pretty  much 
the  same  situation.  The  V.E.'s  are  nearly  equal,  the  A.E.'s  deviate 
in  different  directions  for  the  different  observers,  and  then  only  by 
4  or  5  per  cent. 

The  idea  of  a  direct  sense  for  velocity  is  not  a  new  one,  having 
been  suggested  by  Woodworth  and  asserted  by  Jaensch.  That  the 
perception  of  extent  is  influenced  by  the  speed  of  the  movement  was 


62  THE   IXACCURACT    OF    MOVEMENT 

long  ago  demonstrated  by  Goldseheider,  who  found  the  limen  to 
decrease  as  the  rapidity  of  movement  increased.  After  the  sensations 
of  strain  and  resistance,  the  sensations  attending  different  velocities 
seem  to  afford  the  closest  approximation,  in  the  perception  of  move- 
ment, to  a  graduated  intensive  series,  and  the  actual  existence  of 
such  a  series  is  easily  observed  introspectively.  Intensive  differences 
in  the  sensations  localized  chiefly  in  the  elbow  joint  can  be  distinctly 
felt  in  making  the  same  forearm  movement  at  different  velocities. 
The  fact  that  the  limen  decreases  with  higher  rates  of  movement 
indicates  the  intensifying  effect  of  speed  on  a  subliminal  stimulus, 
and  if,  as  introspection  shows,  changes  in  velocity  exert  this  intensi- 
fying influence  on  supraliminal  sensations  as  well,  we  have  provided 
a  thoroughly  adequate  basis  for  direct  perceptions  of  speed,  without 
reference  to  the  elements  of  either  extent  or  duration.  Although, 
physically,  the  calculation  of  velocity  involves  a  relation  of  distance 
and  duration  {V ^^S/T),  the  judgment  in  consciousness  may  not  be 
made  in  terms  of  such  a  formula.  The  assertion  of  a  "special  sense" 
for  speed  must  not  be  misunderstood  nor  carried  too  far.  It  is  a 
"special  sense"  in  the  same  way  that  the  perception  of  the  position  of 
our  limbs  is  mediated  by  a  "special  sense."  The  statement  means 
merely  that  among  the  manifold  qualities,  intensities  and  interrela- 
tions of  sensations  afforded  by  movements  of  the  limbs,  certain  have 
become,  through  long  experience,  associated  so  intimately  with  speed 
differences  that  the  passage  from  quality,  intensity  and  interrelation 
of  sensation  to  judgment  of  speed  no  longer  follows  a  round-about 
path  of  inference  which  may  or  may  not  once  have  been  necessary, 
but  is  direct  and  immediate— an  empirical  system  of  speed  signs  has 
been  evolved.  Given  a  movement  in  process  of  execution  and  the 
possibility  of  knowing  the  position  of  my  limb  at  a  given  point,  I  am 
able  to  tell,  apparently  from  the  intensity  of  certain  movement  sen- 
sations at  the  point  in  question,  the  approximate  or  relative  speed  of 
my  movement,  without  reference  to  the  actual  or  subsequent  extent 
of  the  movement  or  to  the  time  elapsed  since  its  initiation.  Indeed 
the  speed  up  to  the  time  of  judgment  may  have  been  irregular.  The 
present  speed  may  have  begun  only  a  moment  before  my  judgment 
is  made,  and  may  bear  no  relation  at  all  to  the  total  extent  or  dura- 
tion of  the  movement.  The  anatomical  source  of  the  sensations  on 
the  intensity,  quality  or  interrelations  of  which  the  judgment  is  based 
need  not  concern  us  in  this  connection. 


CHAPTER   V 

Memory  for  Extent  and  Duration 

While  performing  the  experiments  on  the  relation  between  the 
extent  and  duration  of  movements  occasion  was  taken  to  observe  the 
effect  on  accuracy  of  the  interval  elapsing  between  the  standard 
movement  and  the  attempt  to  reproduce  it.  Among  the  many  re- 
searches on  sense  memory  that  have  been  reported  several  include 
experiments  on  extent  and  direction  of  movement  and  on  the  move- 
ment sensations  involved  in  lifting  weights.  Less  attention  has  been 
given  to  the  question  of  memory  for  time  intervals.  A  brief  review 
of  the  chief  studies  in  which  memory  for  magnitudes  in  the  percep- 
tion of  which  the  sense  of  movement  is  involved  will  serve  to  intro- 
duce the  results  of  the  present  experiments  on  this  point. 

Cattell  and  Fullerton/  in  studying  memory  for  lifted  weights, 
employed  the  method  of  right  and  wrong  cases  on  ten  observers,  using 
a  normal  weight  of  about  100  grams  and  a  difference  of  8  grams. 
Seven  intervals  were  used,  ranging  from  1  to  61  seconds.  The  ap- 
proximate probable  error  did  not  seem  to  increase  so  long  as  the 
interval  did  not  exceed  9  seconds,  but  beyond  this  point  increased  by 
about  one  third,  but  again  remained  rather  constant  for  the  intervals 
of  15,  31  and  61  seconds.  "The  memory  image  seems  to  last  up  to 
9  seconds,  after  which  the  observer  does  not  so  much  compare  the 
sensations  as  decide  on  the  approximate  intensity  of  each  sensation 
separately  and  compare  the  decisions. ' '  Lewy-  investigated  memory 
for  the  length  of  visual  lines  ranging  from  20  to  200  mm.,  using  9 
intervals  between  1  and  60  seconds.  The  error  was  found  to  increase 
with  the  length  of  the  interval,  slowly  up  to  10  seconds  and  then  more 
rapidly,  though  it  was  greater  at  1  second  than  at  2.  Th.  Schneider^ 
worked  with  curvilinear  movements  of  the  hand,  rotating  on  the 
wrist  joint.  The  standard  was  given  by  the  method  of  "impact" 
and  6,000  experiments  were  made  on  three  subjects  by  the  method  of 
average  error  of  reproduction.  The  magnitudes  lay  between  70  and 
100  mm.  and  the  intervals  varied  from  i  to  15  minutes.  Up  to  2 
minutes  the  error  remained  quite  constant  (about  3  per  cent),  then 
increased  slowly  to  5^  per  cent,  after  an  interval  of  15  minutes. 
Delabarre*  made  a  few  preliminary  tests  on  the  influence  of  time 

1 "  Small  Differences,"  p.  147. 

'Zeit.  f.  Psychol,  u.  Physiol,  d.  Sinn.,  8,  230,  1895. 

'"La  Memoire  des  Mouvements  Actifs,"  Diss.,  Juriew,  1894. 

* "  Bewegungsempfindungen,"  105.  "  , 

or! 


64  THE   INACCURACY    OF    MOVEMENT 

interval.  He  found  4  seconds  to  be  the  most  favorable  period,  though 
wide  deviations  ranging-  to  29  seconds  are  said  to  have  made  no  ap- 
parent difference.  Jastrow^  found  memory  for  both  visual  and 
tactual  extents  to  be  extremely  accurate  and  to  be  almost  as  faultless 
after  a  lapse  of  several  days  as  after  a  few  minutes.  Miinsterberg® 
reports  experiments  by  Slatopolski  on  memory  for  vertical  move- 
ments (5  to  50  cm.)  of  the  arm.  Intervals  of  1  to  60  seconds  were 
employed  on  four  subjects,  the  standard  being  given  by  the  method 
of  ' '  impact. ' '  The  average  error  of  reproduction,  which  varied  from 
10  per  cent,  to  100  per  cent,  with  the  magnitude  of  the  standard,  was 
found  to  decrease  until  the  interval  of  10  seconds  was  reached,  after 
which  it  increased  again,  being  about  the  same  for  1  minute  as  for 
1  second. 

Landau''^  performed  a  great  many  experiments  on  memory  for  the 
extent  of  active  and  passive  movements,  using  three  observers,  and 
testing  accuracy  of  recognition  after  intervals  ranging  from  10  sec- 
onds to  6  minutes.  He  claims  to  have  found  the  error  to  be  quite 
uniform  for  intervals  of  less  than  1  minute,  but  to  increase  consid- 
erably after  3  or  4  minutes.  His  tables,  however,  show  a  pretty 
regular  decrease  in  the  percentage  of  right  cases,  from  about  73  per 
cent,  at  10  seconds  to  a  chance  relationship  at  5  minutes.  Weber,^ 
Courtier,''  Vaschide^"  and  Beaunis^^  have  also  reported  more  or  less 
complete  experiments  on  memory  for  extent. 

On  the  question  of  memory  for  time  intervals  the  early  experi- 
ments of  Paneth^-  are  the  only  ones  I  have  been  able  to  find  recorded. 
He  found  that  the  "sharpness  of  the  memory  image"  of  such  inter- 
vals decreases  so  little  in  5  minutes  that  no  change  could  be  detected. 
Larger  intervals  were  not  tried.  Kennedy,  reviewing  the  experi- 
mental work  on  memory  up  to  1898,  concludes  that  "while  memory 
for  words,  pitch,  space,  etc.,  falls  off  rapidly  in  respect  to  accuracy 
as  the  time  interval  increases,  memory  for  time  itself,  so  far  as  has 
been  investigated,  shows  almost  no  diminution  of  accuracy  as  the 
time  interval  increases.  "^^ 

Extent.— In  the  present  series  of  experiments  memory  for  extent 
was  studied  in  the  case  of  four  observers.     With  three  of  these  the 

»  Mind,  11,  552,  1902. 

^Beitrage,  4,  69-88. 

'  Wissench.  Rev.,  1896. 

*  Wagner's  "  Handworterbuch  rler  Physiol.,"  3,  p.  2. 

» "  Drit.  Int.  Cong.  f.  Psychol.,"  1896,  238. 

^*Ibid.,  454. 

"  Rev.  Philos.,  25,  369. 

^Ceniralhl.  f.  Physiol,  4.  81-83,  1890. 

^"PsycJwI.  Rev.,  5,  483,  1898. 


MEMORY   FOR    EXTENT    AND    DURATION  65 

standard  magnitudes  ranged  from  100  mm,  to  400  mm.,  and  the  con- 
tinuous method  was  used,  the  terminal  point  of  the  first  movement 
serving  as  the  starting  point  for  the  second.  With  the  fourth  ob- 
server the  magnitudes  ranged  from  150  mm.  to  600  mm.  and  the 
"successive"  method  was  used,  the  arm  being  returned  to  its  initial 
position  after  passing  over  the  standard  distance,  the  two  movements 
being  thus  made  over  the  same  stretch  of  track.  Five  different  inter- 
vals were  used,  viz.,  2,  5,  10,  15  and  30  seconds,  the  interval  being  in 
each  case  the  time  between  the  termination  of  the  standard  and  the 
beginning  of  the  reproduction.  The  signal  from  the  sound  hammer 
served  to  determine  the  magnitude  of  the  standard.  The  intervals 
were  measured  by  the  swings  of  a  seconds-pendulum,  the  "Now"  of 
the  operator  being  the  signal  for  the  beginning  of  the  second  move- 
ment. After  the  reproduction  the  observer  guessed  as  to  the  prob- 
able direction  of  his  error  by  judging  whether  it  was  "greater"  or 
"less,"  The  car  was  then  returned  to  the  starting  point  and  the 
next  trial  made.  In  order  to  avoid  fatigue  in  the  extended  arm  in 
the  case  of  the  long  intervals  a  horizontal  desk-like  shelf  was  placed 
along  the  track  on  the  observer's  side,  at  a  height  which  allowed  the 
hand  and  wrist  to  be  supported  while  the  car  remained  in  position. 
The  finger  could  thus  be  raised  from  the  car  and  the  feeling  of  cramp 
relieved. 

In  the  calculation  of  error  the  magnitudes  have  been  arranged  in 
5  or  6  groups — 100  mm.  to  150  mm.,  150  mm.  to  200  mm.,  etc.  In 
the  case  of  three  subjects  15  magnitudes,  falling  between  the  upper 
and  lower  limits  of  each  group,  were  given  for  each  interval,  making 
75  trials  of  each  interval  for  observer  L.  and  90  for  each  interval 
with  W.  and  H.,  making  totals  of  375  trials  for  L.  and  450  each  for 
W.  and  H.  In  the  case  of  Bt.  50  trials  for  each  interval  were  given, 
making  250  trials.  The  per  cent,  error  for  each  trial  was  calculated 
and  the  individual  errors  averaged  to  get  the  group  average.  This 
final  error  was  then  analyzed  into  constant  and  variable  errors.  The 
grand  average  for  the  total  rafige,  for  each  interval,  was  then  com- 
puted and  is  indicated  in  the  following  curves. 

The  particular  errors  for  each  observer  may  be  found  in  the 
proper  table  in  Chapter  IV, 

The  results  from  all  four  subjects  are  quite  uniform.  A  state- 
ment of  the  general  tendency  will  depend  chiefly  on  which  one  of 
the  three  measures  of  error  Ls  chosen.  In  all  three  cases  the  gross 
average  error  of  reproduction  increases  in  general,  with  the  length 
of  the  interval.  All  three  show  an  increase  of  gross  error  after  2 
sec,  which  either  falls  slightly  or  remains  constant  at  about  15  sec. 
After  this  point  the  curves  for  the  A.E.  no  longer  agree,  those  for 


66 


TEE    INACCURACY    OF    MOVEMENT 


4* 

/o- 

6--       / 


10- 


10 


/6^     \ 


do 


V 


^•-  Li. 


30 


/O         /d^ 

Fig.  2.     Memory  for  Extent.     Curves  showing  increase  in  error  with 
increasing  interval  between  standard  and  reproduction. 


MEMORY   FOR   EXTENT    AND    DURATION 


67 


A.E. 

C.E. 

V.C. 


Fig.  3.     Memory  for  Duration.     Curves  showing  increase  in  error  with 
increasing  interval  between  standard  and  reproduction. 


68 


THE   INACCURACY   OF    MOVEMENT 


H.  and  Bt.  remaining  on  about  the  same  level,  that  for  L.  rising  to 
its  previous  maximum,  while  that  for  W.  rises  considerably.  But 
these  effects  all  appear  to  be  due  to  the  constant  error,  the  curves 
for  which  are  seen  to  have  the  same  general  direction.  The  C.E. 
becomes  more  positive  up  to  10  or  15  sec,  and  then  falls  again, 
becoming  either  a  smaller  positive  error  or,  as  in  the  case  of  W., 
considerably  negative.  The  variable  error,  however,  seems  to  be 
only  slightly,  if  at  all,  affected  by  the  increase  in  time  interval. 
For  L.  the  level  is  practically  uniform,  for  H.  the  only  considerable 
increase  is  at  30  sec,  while  for  W.  the  errors  at  2  sec.  and  at  30  sec. 
are  slightly  lower  than  the  level  of  the  other  three  points;  Bt.'s  V.E., 
however,  increases  regularly,  from  15  per  cent,  at  2  sec.  to  26  per 
cent,  at  30  sec.  Since  these  tests  were  extended  over  a  considerable 
period  of  time  the  changes  in  the  constant  error  may  easily  enough 
be  due  to  factors  other  than  the  variation  of  the  time  interval. 
Usually  the  trials  made  in  a  given  sitting  were  for  one  or  at  most 
three  intervals,  the  memory  problem  being  rather  incidental  to  the 
experiment  proper.  Under  the  circumstances  the  variable  error 
is  the  most  reliable  measure  of  accuracy.  From  its  relative  con- 
stancy we  may  conclude  that,  within  the  limits  of  the  investigation, 
the  accuracy  of  reproduction,  as  measured  by  the  variable  error,  is 
not  influenced  by  changes  in  the  time  interval.  This  conclusion 
seems  to  be  further  confirmed  by  the  fact  that  the  proportion  of 
right  to  wrong  guesses  does  not  decrease  as  the  time  interval  length- 
ens. Such  slight  change  as  does  occur  is  on  the  whole  in  the  reverse 
direction,  the  proportion  of  right  to  wrong  guesses  increasing  slightly 
for  the  longer  intervals  (see  Table  XXIII.).  In  the  case  of  Bt., 
indeed,  this  increase  is  rather  striking. 

Time,— The  procedure  in  the  experiments  on  memory  for  dura- 
tion was  the  same  as  in  those  on  extent.  The  standard  magnitudes 
ranged  from  1  sec  to  3^  sec,  and  have  been  classified  under  five 
groups.  The  calculation  here  was  the  same  as  in  the  case  of  extent. 
The  subjects  were  W.,  H.  and  Bt.,  and  75  trials  were  made  for  each 
interval  between  the  standard  and  the  reproduction.  The  contin- 
uous method  was  used,  the  standard  duration  being  determined  as 
before,  by  the  checking  of  the  movement  at  the  signal  from  the 
sound  hammer.  At  the  word  of  the  operator,  after  the  appropriate 
interval,  the  observer  went  on  to  reproduce  the  duration  of  the 
standard  movement,  and  guessed  as  to  the  probable  direction  of  his 
error.  The  results  are  shown  in  curves  6,  7  and  8,  and  in  the 
appropriate  tables  in  Chapter  IV.  Here  again  the  three  observers 
agree  pretty  closely.  A.E.'s  and  C.E.'s  increase  up  to  10  sec  Of 
course  the  determining  factor  here  is  the  C.E.  for  changes  in  the 


MEMORY   FOR   EXTENT   AND    DURATION 


69 


A.E.  merely  reflect  changes  in  the  C.E.  In  all  three  cases  the  C.E, 
drops  at  15  sec,  rising-  again  with  H.  and  Bt.,  to  the  maximum  at 
30  sec,  but  dropping  still  further  in  the  case  of  "W.  The  V.E. 
undergoes  little  change.  That  for  "W.  remains  on  practically  the 
same  level  throughout,  agreeing  with  the  results  of  Paneth's  experi- 
ments. With  Bt.  and  H.  there  is,  however,  a  rather  uniform,  though 
slight,  decrease  in  accuracy,  the  V.E.'s  increasing  from  12  per  cent, 
to  17  per  cent,  with  Bt.  and  from  8  per  cent,  to  16  per  cent,  with  H. 


TABLE    XXIII 
Pbopobtion  of  Right  to  Wbong  Guesses  with  Inceeasing  Intebval 


2  sec. 

5  sec. 

10  sec. 

15  sec. 

30  sec. 

L. 

1.2 

0.9 

1.8 

1.5 

1.9 

W. 

1.1 

1.8 

1.7 

2.2 

0.8 

Extent. 

H. 

1.0 

1.2 

1.0 

1.3 

1.5 

Bt. 

2.0 

].4 

2.4 

2.7 

3.3 

W. 

1.0 

0.7 

0.6 

0.8 

1.1 

Time. 

H. 

0.8 

0.7 

1.6 

1.6 

1.1 

Bt. 

0.7 

3.0 

1.7 

1.8 

1.5 

In  these  two  cases  the  loss  of  accuracy  accords,  on  the  whole,  with 
the  "law  of  forgetting,"  as  it  is  usually  stated,  the  error  increasing 
rapidly  at  first  and  then  more  slowly.  Here,  as  in  the  case  of  ex- 
tent, the  proportion  of  right  to  wrong  guesses  fails  to  indicate  any 
decrease  in  accuracy  of  memory  (see  Table  XXIII.).  For  W.  the 
proportions  remain  quite  constant,  for  H.  there  is  a  considerable 
increase  in  the  proportion  of  right  giiesses  as  the  interval  is  length- 
ened, while  for  Bt.  the  minimum  is  at  2  sec,  the  maximum  at  5  sec, 
the  proportion  for  the  greater  intervals  remaining  equal. 


CHAPTER   VI 

Influence  of  the  Degree  of  Contraction 

One  of  the  points  on  which  various  writers  have  differed  is  a 
phenomenon  first  noted  by  Loeb.^  He  found  that  short  movements 
executed  in  different  portions  of  the  possible  range  of  rotation  of  a 
joint  are  not  estimated  with  equal  accuracy.  In  his  experiments  the 
movement  made  under  conditions  of  less  contraction  of  the  acting 
muscle  was  underestimated  as  compared  with  one  made  under  a 
greater  degree  of  contraction.  This  fact  was  used  by  Loeb  in  sup- 
port of  the  theory  of  innervation.  He  held  that  the  objective  short- 
ness of  the  second  movement  was  to  be  explained  by  supposing  that, 
by  virtue  of  the  partial  contraction  already  involved  in  making  the 
first  movement,  further  contraction  was  more  difficult.  As  a  coi>- 
sequence  the  same  innervation  produced  a  smaller  change,  but  since 
equal  innervations  were  made  or  intended,  the  two  movements  ap- 
peared of  equal  length. 

Kiilpe  denies  the  validity  of  Loeb's  figures  and  ascribes  the  sup- 
posed phenomenon  to  *' erroneous  evaluation  of  experimental  re- 
sults. "^  Delabarre^  suggests  that  the  results  are  probably  reliable 
and  explains  them  on  the  basis  of  the  supposed  greater  difficulty  of 
the  movement  under  greater  degree  of  contraction.  But  this  feeling 
of  greater  difficulty  does  not,  for  Delabarre,  involve  innervation 
feelings.  However,  he  finds  the  illusion  to  occur  only  under  con- 
siderable differences  of  contraction.  Angier*  finds  it  not  to  occur 
under  any  circumstances.  Kramer  and  Moskiewicz^  find  the  illusion 
always  to  occur,  and  in  varying  positions  and  directions  of  move- 
ment. They  explain  it  by  the  principle  of  unfamiliarity,  the  theory 
being  that  in  the  unfamiliar  position  the  hand  makes  slower  move- 
ments which  are  thus  made  shorter  in  order  to  be  equal  to  longer 
movements  made  more  quickly.  Since  the  sensation  complexes  are 
different  in  the  two  cases  the  comparison  must  be  made  on  the  basis 
of  some  common  quality.  The  only  common  quality  present  is  the 
duration.  Consequently  these  investigators  surmise  that  the  dura- 
tions of  the  two  movements  are  equal  when  the  extents  appear  to  be, 

^Pfliigers  Archives,  46,  1-46,  1890. 
'  "  Outlines  of  Psychology,"  p.  342. 
^  "  Bewegungsempfindungen,"  p.  90. 
*  Zeit.  f.  Psi/cJiol,  39,  430,  1905. 
^Ibid.,  25,  101-125,  1901. 

70 


INFLUENCE    OF   DEGREE   OF    CONTRACTION 


71 


but  they  made  no  attempt  to  support  their  theory  by  actual  measure- 
ment of  the  time. 

Woodworth^  takes  exception  to  the  form  of  the  preceding  gen- 
eralizations. His  results  show  that  of  the  introspeetively  equal  seg- 
ments of  the  total  excursion,  the  objectively  greater  extents  do  not 
occur  at  the  beginning  but  in  the  middle,  while  the  movements  at 
both  extremes  are  overestimated,  i.  e.,—are  shorter  in  execution. 
Woodworth  accepts  Delabarre's  suggestion  of  the  relative  ease  of 
performance.  Myers'^  accepts  Woodworth's  form  of  the  illusion 
and  Delabarre's  explanation. 

The  following  experiments  were  performed  in  order  to  confirm 
either  Loeb's  or  Woodworth's  results  or  to  show  that  no  constant 
errors  are  to  be  found,  and  to  test  the  "equal  duration"  hypothesis 

TABLE    XXIV 
Extent  of  Successive  Movements  Intended  to  be  Equal 


.5^. 

.^. 

.'^i 

^ 

a 

* 

■t 

mm. 

A.D.  mm. 

A.D. 

mm. 

A.D. 

mm. 

A.D.  mm. 

A.D. 

mm. 

A.D. 

mm. 

A.D. 

E. 

321 

8 

257 

5 

223 

7 

1. 

W. 
B. 

260 
232 

12 
9 

279 
272 

13 
6 

240 
232 

SI 

7 

II. 

R. 

203 

13 

201 

7 

175 

6 

166 

4 

W. 

207 

15 

246 

10 

228 

10 

196 

10 

R. 

162 

13 

156 

12 

134 

10 

123 

8    110 

10 

115 

11 

99 

fi 

W. 

139 

16 

158 

13    166 

13  1  149 

13    131 

11 

126 

10 

III. 

B. 

105 

14  i  122 

9  1137 

75  i  129 

2\l\Q 

9 

95 

7 

89 

7 

Bt. 

156 

15  1  177 

19  .  143 

11    132 

9,108 

9 

103 

8 

V. 

158 

8   171 

10    161 

2    139 

.9  126 

11 

116 

10 

C. 

136 

10   140 

13  i  140 

10   121 

8\  111 

9 

124 

8 

TABLE    XXV 
DuEATioN  OF  Movements  whose  Extent  is  Shown  in  Table  XXIV 


.i^, 

.5^. 

*, 

li 

* 

i 

I' 

sec. 

A.D. 

sec. 

A.D. 

sec. 

A.D 

sec. 

A.D. 

sec. 

A.D. 

sec. 

A.D. 

sec.  A.D. 

E. 

3.13 

9 

2.97 

11 

3.14  10 

I. 

W. 
B. 

1.38 
L12 

38 
13 

1.32 
.96 

35 
10 

1.39  35 
.92  9 

IL 

E. 

2.28 

19 

2.13 

9 

2.08 

7 

2.24  15 

W. 

1.34 

37 

1.14 

33 

L16 

41 

1.35  4^ 

E. 

2.16 

u 

2.09 

SO 

2.07 

SI 

2.08 

SI 

1.93 

18 

2.17 

18 

1.97  27 

W. 

1.10 

35 

1.20 

S5 

L15 

33 

1.04 

55 

1.00 

32 

1.08 

35 

III. 

B. 

1.12 

14 

1.03 

15 

1.00 

15 

.97 

9 

.91 

12 

.78 

10 

.86  9 

Bt. 

.89 

8 

.95 

12 

.88 

14 

.87 

13 

.83 

11 

.85 

IS 

V. 

.80 

15 

.76 

17 

.70 

11 

.68 

10 

.68 

15 

.67 

9 

C. 

.80 

11 

.75 

IS 

.76 

13 

.70 

13 

.71 

11 

.75 

11 

° "  The  Accuracy  of  Voluntary  Movement,"  p.  79. 

^  "  Experimental  Psychology,"  p.  73.     Longmans,  1909. 


72  THE   INACCURACY    OF    MOVEMENT 

of  Kramer  and  Moskiewicz.  The  experiment  consists  of  three  series, 
in  all  of  which  the  extents  were  recorded  in  millimeters  and  the 
durations  in  hundredths  of  a  second. 

In  Series  I.  the  total  excursion  was  divided  into  three  movements 
of  introspectively  equal  extents,  in  Series  II.  into  four  such  move- 
ments. In  Series  III.,  after  a  few  preliminary  trials  in  order  to 
get  the  total  number  of  movements  into  the  single  excursion,  the 
subject  made  six  (in  two  cases  seven)  successive  movements,  here 
again  of  apparently  equal  length.  In  cases  E.,  AY.  and  B.  the 
length  of  the  interval  between  movements  Avas  left  entirely  to  the 
preference  of  the  subject.  In  cases  Bt.,  Y.  and  C,  each  movement 
was  made  at  a  signal  by  the  operator.  In  this  way  it  was  possible 
to  vary  the  interval  between  movements  and  thus  avoid  any  tendency 
to  mere  rhythmical  performance  on  the  part  of  the  subject.  Series 
I.  and  II.  show  the  average  results  of  10  trials  and  Series  III.  of  20 
trials  for  each  subject,  a  total  of  930  movements.  Tables  XYIY. 
and  XXY.  give  the  average  movement  in  each  position,  in  milli- 
meters, and  its  average  deviation  in  per  cent,  for  both  extent  and 
duration.  Table  XXVI.  gives  the  average  of  the  first  movements 
and  the  positive  or  negative  deviation  (A.E.)  in  per  cent,  of  each 
of  the  successive  movements  from  this  average,  both  for  extent  and 
duration  as  well  as  the  variability  (Y.E.)  of  all  the  movements  from 
their  average. 

Extent.— In  Series  I.,  for  both  "VY.  and  B.,  the  middle  segment  is 
longer  than  either  the  first  or  third.  In  Series  II.,  for  W.,  both  the 
second  and  third  segments  are  longer  than  either  the  first  or  fourth. 
In  Series  III.,  except  for  subject  R.,  and  one  additional  instance,  the 
first  segment  is  shorter  than  either  the  second  or  third  and  in  two 
cases  than  the  fourth  segment,  while  beyond  the  approximate  middle 
of  the  excursion  the  segments  decrease  again,  still  more  rapidly  than 
they  increased  at  the  beginning.  Thus  in  all  but  one  subject  the 
results  correspond  with  those  obtained  by  AYoodworth.  The  diverg- 
ence in  the  case  of  R.  is  probably  due  to  the  fact  that  of  the  six 
subjects  he  was  by  far  the  tallest  and  had  the  longest  arm.  The 
range  employed  did  not  constitute  his  maximum  excursion,  and  from 
the  position  assumed  before  the  apparatus  the  first  part  of  the  total 
swing  was  the  part  not  used.  The  degTee  of  contraction  of  any  one 
muscle  or  single  set  of  muscles  does  not  afford  adequate  basis  for 
generalization,  even  disregarding  the  fact  that  somewhat  different 
sets  are  likely  to  be  employed  in  the  execution  of  different  segments. 
It  should  also  be  noted  that  these  results  are  just  the  reverse  of 
what  one  should  expect  if  the  judgment  of  extent  were  based  on  the 
angle  of  rotation  at  the  joint.     For  the  same  angle,  reproduced  at 


INFLUENCE    OF   DEGREE   OF    CONTRACTION 
TABLE    XXVI 


(M  iM  CO       "^  OO       CO  iC  O  CO  O  CO 


iC 


•;n9f)  J8J  -g-y 


lO 


kC 


eo  ©q  (M     «o  05     lO  «o  ic  CO  IN  00 


CO  t^  I> 

O  O  00       (MO       05        CO 


++I 

1  + 

1    1 

O  (N  O  ^  «0  O 
CO          rH 

+ 1  1  1  1  1 

OS  CO 
I— t 

1  1 

O  Oi  OS  t>  lO  i-H 

l-H            1—1            rH   I-H 

1  1  1  1  1  1 

lO  -"S*  iC 

1  1  1 

Tt<  u5  eo  <N  lo  CO 

r-l          I-H  T-H 

M 

Tji  IC  l-H  rH  C<1  lO 

1—1          I— 1 

1    +    1       1       1       1 

CO  05  OO  t-  IlO  o 

l+l+l I 


•08S  1  ^mfi 


C<)  1— (       C<)  I— I  I— ( 


■ina'->  lajT  -rj- A  COOOO       OiO       ICOJCOCDCOCO 


•■tnao  jaj  -a-y 


•inni  X  '■Jian. 
•paBpuB^s 


'JdAjasqo 


1+       i     1  + 


++I     I 


o  CO     t^  OS  o  00  IN  eo 

1—1  1— I  rH  CO 

I ++ I ++ 


+ 


•*  eo  CD  N  00  00 
1—1  1—1 1— I 

I +++++ 


T-lOIN  eOl^  (NCJiOCOCOCO 
INCOCO  OIN  ^COOiCiOCO 
eOC-IIN        IN  IN        i-li-(i-li-lrHrH 


W^pq    p4^    p4^P0pq>d 


73 


74  THE   INACCURACY    OF    MOVEilEXT 

the  shoulder  joint,  would  mean  a  greater  movement  at  the  extremes 
of  this  total  rectilinear  excursion  than  in  the  middle,  and  in  the 
attempt  to  reproduce  extent  the  middle  segments  would  be  shorter, 
those  at  the  extremes  longer. 

Duration.— In  the  ease  of  the  times  the  segments  never  increase 
throughout  the  total  excursion.  On  the  other  hand,  in  7  cases  the 
extreme  segments  are  greater  than  the  intermediate.  This  indicates 
a  tendency  for  the  extreme  segments,  both  initial  and  terminal,  to 
be  greater  and  the  intermediate  less  than  the  average  of  the  group. 
This  is  especially  clear  in  Series  I.  and  II.,  where  the  differences  in 
degree  of  contraction  for  the  separate  movements  are  greater.  Corre- 
lating {r  =  cos7rV)  the  extents  with  the  durations  of  the  respective 
segments,  we  get  the  following  coefficients: 

Bt.  V.  C. 


Observer. 

B. 

W. 

B. 

Series     I. 

r  = 

+  .51 

—  .51 

—  .51 

II. 

r  = 

0 

—  .71 

III. 

r  = 

+  .43 

+  .71 

+  .61 

+  .97  +  .86  +  .86 

When  the  differences  between  the  positions  of  the  successive  seg- 
ments are  considerable,  as  in  Series  I.  and  II.,  the  correlation  is 
negative— the  longer  movements  occupy  the  shorter  times,  but  when 
the  differences  in  position  are  less,  as  in  Series  III.,  the  correlation 
is  positive— extents  and  durations  tend,  on  the  whole,  to  vary  in  the 
same  direction. 

Inspection  of  the  average  deviations  of  the  individual  movements 
from  their  averages,  as  shown  in  Tables  XXIV.  and  XXV.,  shows 
that  the  extents  included  in  any  given  segment  average  are  much 
more  constant  and  uniform  than  the  durations.  That  is,  their  aver- 
age deviations  from  the  average  of  their  respective  groups  are 
smaller,  the  grand  average  for  extent  being  only  10  per  cent,  as 
against  19  per  cent,  for  duration.  This  difference,  however,  is  not 
particularly  significant,  since  no  special  effort  was  made  to  keep  equal 
the  magnitudes  ranging  around  a  given  segment.  Moreover,  there 
was  more  chance  for  variation  in  the  time  than  in  the  extent,  since 
the  observer's  attention  was  never  explicitly  called  to  the  duration 
of  his  movements  and  there  was  no  attempt  to  keep  the  speed  con- 
stant. The  attempt  was  always,  having  made  a  first  movement,  to 
make  all  succeeding  movements  of  the  excursion  in  question  equal 
in  extent  to  this  first,  without  reference  to  the  magnitude  of  corre- 
sponding segments  of  other  excursions. 

Table  XXVI.  shows  the  relative  accuracy  of  this  performance 
with  respect  to  the  deliberate  extents  and  the  incidental  times  as 
well.     In  this  table  the  A.E.  represents  the  average  deviation  from 


INFLUENCE    OF   DEGREE   OF    CONTRACTION  75 

the  standard,  while  the  V.E.  represents  the  per  cent,  variation  from 
the  average  of  all  the  segments  of  the  group.  The  final  A.E.  and 
V.E.  for  extent  (14  per  cent,  and  11  per  cent.)  are  twice  as  large  as 
the  corresponding  errors  for  duration  (7  per  cent,  and  5  per  cent.). 
The  durations  are  more  nearly  equal  than  the  extents,  just  as  was 
the  case  in  Chapter  IV.  As  the  figures  stand,  they  tend  pretty 
strongly  to  confirm  the  conjecture  of  Kramer  and  Moskiewicz. 

But  this  closer  agreement  does  not  in  itself  suffice  to  demonstrate 
the  perception  of  time  to  be  any  more  fundamental  than  the  percep- 
tion of  extent.  As  in  most  cases  of  naturally  reproduced  movements, 
there  is  a  tendency  to  repeat  the  whole  original  performance  (see 
Chapters  II.  and  IV.),  reproducing  both  duration  and  extent.  In 
this  case  factors  enter  which  disturb  the  spatial  judgment  but  do  not 
affect  the  temporal.  The  times  are  more  nearly  equal,  not  because 
they  constitute  a  common  factor  which  serv^es  as  a  basis  of  com- 
parison in  reproducing  extent,  but  simply  because  the  change  in. 
position  of  the  moving  member  introduces  no  factors  which  affect 
the  judgment  of  duration.  There  is  indeed  no  reason  for  supposing 
the  perception  of  time  to  be  based  on  processes  in  the  moving  member. 
It  is  probably  based  instead  on  processes  of  a  more  permanent  and 
regular  sort,  taking  place  in  other  parts  of  the  organism.  But  the 
judgment  of  extent  is  subject  to  every  local  change  in  position,  strain, 
ease  of  movement,  familiarity,  inertia,  etc. 

In  producing  the  illusion  of  extent  all  the  factors  mentioned  by 
the  earlier  writers  are  probably  effective,  allowing  for  the  modifica- 
tion of  Loeb's  "innervation"  theory  made  by  contemporary  psy- 
chology. These  factors  seem  to  fall  into  two  groups:  (1)  conditions 
of  performance  and  (2)  conditions  of  perception. 

1.  Conditions  of  Performance.— It  may  be  supposed  that  the  first 
movements  of  the  series  are  more  difficult  than  later  ones,  since  the 
inertia  of  the  musculature  has  to  be  overcome  in  the  one  case  but  is 
already  removed  in  the  other.  In  the  middle  portion  of  the  excur- 
sion movements  are  more  easily  made,  since  the  muscle  is  already 
warmed  up  and  in  action.  "While  at  the  terminal  end  of  the  excur- 
sion it  may  be  supposed  that  movement  is  more  difficult  than  in  the 
middle  portion  because  of  the  greater  degree  of  contraction,  entailing 
greater  innervation,  or  because  of  the  unfamiliarity  of  the  movement. 
This  last  factor  may  affect  both  ends  of  the  series.  Movements  here, 
being  less  familiar,  and  the  signs  which  indicate  extent  being  less 
thoroughly  systematized  and  learned,  tend  to  be  made  with  greater 
caution.  That  they  are  made  more  slowly  is  clear  from  Table  XXVI. 
When  the  duration  of  the  standard  movement  has  elapsed  there  is  a 
strong  disposition  to  feel  the  movement  as  completed,  since  its  tem- 


76  TEE   INAGCVRACT    OF    MOVEMENT 

poral  factor  has  been  approximately  reproduced.  The  movement  is 
thus  stopped  somewhat  short  of  the  proper  extent,  a  kind  of  com- 
promise being  effected  in  which  both  spatial  and  temporal  accuracy- 
are  partially  sacrificed,  the  durations  tending  on  the  whole  to  fall  out 
slightly  too  long  and  the  extents  too  short. 

2.  Co7iditio7is  of  Perception.— Delaharre^s  suggestion  that  any- 
thing which  increases  the  sensory  elements  of  a  movement  increases 
its  apparent  magnitude,  though  untenable  as  a  generalization,  may  be 
applied  here  with  advantage.  There  is  no  doubt,  introspectively,  that 
at  either  extreme  of  the  arm 's  excursion  the  sensations  resulting  from 
a  given  objective  change  in  position  of  the  limb  are  relatively  intensi- 
fied. The  member  is  approaching  its  limit  of  movement,  the  tension 
of  muscles  and  tendons  is  approaching  a  maximum  as  the  degree  of 
contraction  increases,  the  skin  over  the  joint  is  stretched,  the  sub- 
cutaneous tissues  are  more  firmly  compressed  about  the  fulcrum  of 
the  joint.  The  sensory  elements  of  any  movement  made  under  these 
conditions  will  be  relatively  increased  and  in  so  far  as  extent  of 
movement  is  judged  in  terms  of  intensity  of  sensation,  we  should  have 
the  Loeb  illusion  at  both  extremes  of  the  total  swing  without  consid- 
ering the  difficulty  of  performance,  either  as  a  result  of  inertia,  de- 
gree of  contraction  or  unfamiliarity.  IMoreover,  we  would  expect 
more  complete  and  prompt  adaptation  to  the  sensations  aroused  by 
the  more  familiar  movements  in  the  central  portion  of  the  excursion 
and  this  again  would  produce  a  relative  decrease  in  the  sensory  ele- 
ments of  such  movements. 


CHAPTER   VII 

Criteria  of  the  Judgment  of  Extent 

The  greater  part  of  the  work  on  movement  has  been  topograph- 
ical in  motive  and  in  method,  consisting  of  observations  of  motor 
ability  and  accuracy  under  definite  experimental  or  pathological  con- 
ditions or  of  attempts  to  localize  anatomically  the  source  of  the  sen- 
sations on  which  specific  judgments  are  based.  Interesting  as  these 
results  may  be  to  the  physiologist  or  physician,  they  throw  little  light 
on  the  processes  of  discrimination,  recognition  and  comparison  in- 
volved in  our  judgments  concerning  movements.  In  fact  there  seems 
to  be  a  kind  of  "anatomist's  fallacy"  in  such  a  procedure,  at  least 
so  far  as  the  psychology  of  movement  is  concerned,  for  it  seems  to 
proceed  on  the  tacit  assumption  that  the  sensation  is,  psychologically, 
what  it  is  anatomically.  And,  as  we  might  expect,  the  topographical 
procedure  has  led  into  all  kinds  of  disagreement.  Nowhere  is  this 
disagreement  more  apparent  than  in  the  matter  of  the  criteria  or 
differentiae  of  the  judgment  of  extent.  The  chief  cause  of  disagree- 
ment here  seems  to  have  been  the  desire  to  simplify  the  "muscle 
sense,"  to  trace,  if  possible,  the  sensation  of  movement  to  a  single 
anatomical  source.  This  term  "muscle  sense"  has  been  used  to 
designate  the  whole  group  of  articular,  tendinous,  muscular,  cutane- 
ous and  visual  elements  that  go  to  make  up  the  kinesthetic  perception. 
That  the  mere  sensation  of  movement  may  be  mediated  by  any  or  all 
of  these  has  been  pretty  generally  agreed,  but  when  specific  topics 
are  concerned— the  judgments  of  extent,  force,  time  and  direction  of 
movement — opinion  is  not  nearly  so  unanimous. 

After  a  great  number  of  experiments  of  the  topographical  sort, 
Goldscheider^  concluded  that  the  joint  sensations  afford  the  chief 
criteria  for  the  judgment  of  extent  and  direction  of  movement. 
Attempts  were  made  to  get  a  pure  muscle  sensation  isolated  from 
other  elements  of  the  kinesthetic  sensation.  The  skin  over  a  muscle 
was  anesthetized  and  the  muscle  stimulated  electrically.  The  diffuse 
sensation  produced  was  said  not  in  the  least  to  resemble  the  sensa- 
tion of  movement.  When  the  joint  alone  was  anesthetized  the  con- 
sciousness of  movement  became  so  blunt  that  it  was  evident  that  the 
feeling  of  contraction  could  not  be  used  for  fine  discrimination  of 
extents,  while  anesthesia  of  the  skin  produced  no  disturbance  of 
space  perception.      On  the  basis  of  these  and  similar  experiments 

*  A.  Goldscheider,  "  Untersuchungen  iiber  den  Muskelsinn,"  3G9  ff. 

77 


78  THE   INACCURACY    OF    MOVEMENT 

Goldscheider  concludes  that  ' '  muscle  sensations,  which  were  formerly 
accorded  the  leading  role  in  the  cognition  of  weight  and  in  the  estima- 
tion of  the  magnitude  and  direction  of  movement,  do  not  appear  at 
all  except  as  a  result  of  intensive  stimulation,  great  fatigue  or  in  the 
form  of  muscular  pain. ' ' 

Kiilpe-  accepts  Goldscheider 's  conclusion,  with  certain  amplifica- 
tions of  his  own.  "It  may  be  conjectured  a  priori  that  muscular 
and  tendinous  sensations  can  not  form  the  ground  of  our  judgment 
of  the  position  and  movement  of  our  limbs  in  the  absence  of  visual 
perception.  There  is  no  proportionality  between  the  extent  and 
duration  of  a  movement  and  the  possible  concomitant  excitations  in 
muscle  and  tendon. "  "On  the  other  hand,  the  relation  between  the 
positions  of  the  articular  surfaces  as  regards  each  other  and  positions 
or  movements  of  the  limbs  is  just  as  simple  as  that  between  the  dif- 
ferent parts  of  the  skin  or  retina  and  the  points  from  which  they  are 
stimulated.  We  see,  therefore,  that  the  articular  sensibility  fur- 
nishes us  the  real  basis  of  our  perception  of  the  position  and  move- 
ments of  the  limbs  where  an  appeal  to  vision  is  excluded. ' '  Kramer 
and  Moskiewicz  confirm  this  conclusion  by  saying:  "Sensations 
arising  from  the  processes  of  tension  of  the  muscles  are  unessential 
to  inform  us  concerning  the  judgment  of  the  position  or  movement 
involved."^  James,  in  turn,  accepts  the  theory  on  the  basis,  chiefly 
of  Goldscheider 's  results :  ' '  We  indubitably  localize  the  finger  tip  at 
the  successive  points  of  its  path  by  means  of  the  sensations  which  we 
receive  from  our  joints."* 

In  striking  contrast  with  this  position  are  the  more  recent  state- 
ments of  Pillsbury  and  of  Reichardt,  leading  back  to  the  older  posi- 
tion of  Brown  and  Delboeuf.  Reichardt,^  working  on  the  illusions 
of  passive  movement,  claims  that  the  sense  of  position  is  not  mediated 
by  the  part  moved  but  by  processes  in  the  moving  muscle.  Pillsbury® 
finds  that  "the  sensitivity  of  joints  is  decreased  by  induction  currents 
through  the  wrist  and  elbow  as  well  as  through  the  joints  in  question. 
This  fact,  together  with  the  lack  of  anatomical  evidence  that  the 
joints  have  sensory  endings,  makes  it  probable  that  the  sensation  of 
movement  is  derived  mainly  from  the  tendon  and  muscle,  rather  than, 
as  Goldscheider  thought,  from  the  joints." 

Under  the  circumstances,  then,  we  should  expect  somebody  else  to 
abstract  some  other  element  and  exalt  it  into  the  position  of  chief 

^"Outlines  of  Psychology."     London,  Sonnenschein,   1901,  143. 

^Zeit.  f.  Psychol,  25,  105,  1901. 

*  "  Principles  of  Psychol.,"  2,  193. 

^Zeit.  f.  PsycJwl.,  40,  430.  1906. 

^  Amer.  Jour,  of  Psychol.,  12,  346,  1901. 


CRITERIA    OF    THE   JUDGMENT    OF   EXTENT  79 

criterion.  And  this  is  what  occurs.  Bourdon^  finds  that  the  least 
perceptible  tension  of  the  skin  about  the  dorsal  joint  of  the  finger  is 
about  .2  mm.,  and  that  this  is  just  the  tension  required  to  allow  the 
least  perceptible  movement— 1  mm.— to  take  place.  He  also  insists 
that  to  suppose  the  joint  sense  to  be  the  source  of  criteria  for  judg- 
ments of  extent  of  movement  presupposes  for  the  articular  surfaces 
a  tactual  acuity  much  higher  than  that  of  the  skin  in  its  most  sensi- 
tive parts,  and  that  this  contradicts  the  general  rule  that  sensitivity 
decreases  as  we  go  more  deeply  into  the  interior  of  the  body.  Con- 
sequently, he  concludes  that  the  criteria  of  extent  of  movement  are 
in  all  probability  to  be  found  in  the  tensions  of  the  skin  above  the 
moving  joint.  Nevertheless  we  find  Pillsbury  saying:  "That  the 
skin  does  not  serve  as  source  of  the  sensations  which  indicate  move- 
ment may  pass  without  comment. ' ' 

Still  other  facts  tell  against  the  conception  of  the  joint  linings  as 
a  "reduced  map"  of  the  extent  of  movements.  One  is  the  fact  that 
our  movements  do  not  consist  of  simple  joint  movements  in  one  direc- 
tion or  of  combinations  of  such  movements.  Thus  in  the  execution 
of  a  compound  arm  movement  of  any  considerable  magnitude  the 
elbow  joint  tends  to  double  back,  beyond  a  certain  point  in  the  move- 
ment, retracing  its  original  rotation  but  in  the  reverse  direction. 
Particularly  is  this  true  if  the  movement  approximates  the  rectilinear 
type.  As  a  result  of  this  it  follows  that  the  fixed  point-for-point 
correspondence  between  points  on  the  articular  surfaces  and  points 
in  external  space  is  not  so  fixed  as  might  at  first  appear.  A  point  on 
the  membrane  lining  the  shoulder  joint  may  mean  almost  any  point 
in  external  space,  depending  on  the  complex  relation  of  the  positions 
of  elbow,  wrist  and  finger  joints.  If  our  most  common  movements 
or  even  our  earliest  movements  consisted  of  rotations  at  a  single 
joint,  a  point  for  point  correspondence  might  be  established.  But 
such  is  not  the  case.  From  the  genetic  point  of  view  at  least  our 
spatial  order  is  built  up  on  a  basis  of  primitive  and  practical  move- 
ments which  are  complex  in  character  and  mechanism— such  move- 
ments as  brushing  awaj^  a  fly,  pulling  or  pushing  objects  to  or  from 
the  body,  striking  a  blow,  raising  a  lever,  etc.  The  anatomically 
simple  single  joint  movement  comes  to  be  artificial,  for  greater  speed 
and  accuracy  are  undoubtedly  to  be  gained  by  the  complex  movement. 
But  even  with  these  compound  movements  there  might,  it  is  true,  be 
developed  a  system  of  local  signs  on  the  articular  surfaces,  the  com- 
binations and  interrelations  of  which  might  come  to  mean  extent  of 
movement.  Such  a  proposition,  however,  yields  the  whole  argument 
for  the  exclusive  role  of  the  joint  sense  and  affords  no  reason  for 

TAnnee  de  Psychol,  13,  1.33-143,  1907. 


80  THE   INACCURACY    OF    MOVEMENT 

excluding  criteria  afforded  by  sensations  from  muscles,  tendons,  skin 
and  subcutaneous  tissue. 

A  striking  experiment  by  Mtinsterberg^  shows  that  the  same  ex- 
tent of  movement  may  be  represented  in  one  situation  (with  extended 
forearm)  by  a  given  angular  rotation,  in  another  (with  forearm 
flexed)  by  a  rotation  three  or  four  times  as  great.  This  experiment 
alone  should  suffice  to  demonstrate  the  empirical  basis  of  the  judg- 
ment of  extent,  and  to  emphasize  the  importance  of  factors  other 
than  the  number  of  degrees  of  joint  rotation.  Still  further,  what- 
ever importance  one  may  be  disposed  to  attribute  to  eye  movements 
in  the  perception  of  visual  space,  the  fact  remains  that  to  a  certain 
extent,  even  with  closed  eyes  or  in  the  dark  room  we  can  know  with 
a  certain  degree  of  correctness  the  position  of  the  eyes  and  estimate 
the  amount  of  their  movement,  although  there  are  no  articular  mem- 
branes involved. 

An  even  clearer  illustration  is  to  be  found  in  cases  of  acquired 
control  over  the  ear  muscles.  Diligent  practise  since  boyhood  has 
enabled  me  to  perform  either  monaural  or  binaural  movements  with 
considerable  facility  and  has  developed  a  rather  definite  range  of 
recognized  extents.  In  this  case  there  has  been  neither  articular 
surface  nor  even  cooperation  with  visual  criteria.  Movements  of  the 
tongue  are  also  made  with  great  accuracy,  although  we  do  not  ordi- 
narily have  occasion  to  apply  objective  scales  of  measurement  to  them. 

Attempts  to  find  a  single  topographical  or  anatomical  source 
have  thus  been  futile.  Goldscheider 's  experiment,  which  for  James 
"completely  established"  the  role  of  the  joint  sense  is  contra- 
dicted by  Pillsbury's  results.  Adherence  to  Kiilpe's  suggestion 
of  the  accurate  correspondence  of  points  on  articular  surfaces  with 
points  in  external  space  requires  a  tactual  acuity  which  Bourdon 
can  not  accept,  and  nerve  endings  in  the  joint  linings,  which  have 
not  yet  been  satisfactorily  demonstrated.  Reichardt's  attribution 
of  the  sensations  indicating  extent  to  the  processes  taking  place  in 
the  moving  muscle  is  discounted  by  Duchenne's  patients,  in  whom 
insensibility  of  muscles  was  found  along  with  intact  perception  of 
movement.  Bourdon's  attempt  to  refer  the  sensations  to  skin  ten- 
sion over  the  moving  joint  is  contradicted  by  Goldscheider 's  sub- 
jects with  anesthetized  skin  but  unimpaired  perception  of  movement. 
And  these  topographical  attempts  fail  because,  as  it  appears,  sensa- 
tions do  come  from  many  sources  and  any  sensation  which  can  aid  in 
the  differentiation  of  one  movement  from  another  serves  to  identify 
that  movement  when  it  occurs  again. 

More  conciliatory  is  the  statement  of  Delabarre  to  the  effect  that 

^Beitrdge,  1892,  IV.,  178-191. 


CRITERIA    OF    THE   JUDGMENT    OF   EXTENT  81 

* 'movements  are  judged  equal  when  their  sensory  elements  are 
equal,"  although  the  precise  nature  of  such  an  equality  is  not  ap- 
parent. Aside  from  the  possible  tautology  of  the  statement,  it  is 
not  clear  how  such  heterogeneous  elements  as  duration,  speed,  force, 
strain,  position,  are  commensurable.  The  equality  can  hardly  be  of 
an  intensive  character,  for  two  excursions  may  be  equal  in  extent 
and  yet  afford  sensations  of  strain  that  are  exceedingly  dispropor- 
tionate to  the  error  in  apparent  magnitude.  A  better  statement 
Avould  probably  be  the  one  we  have  already  suggested,  viz.,  that 
movements  are  judged  to  be  equal  which  have  been  learned  to  he 
equal — that  judgment  and  discrimination  are  not  based  on  anatomy, 
nor  even  on  an  intensive  psychophysical  relation  between  magnitude 
of  stimulus  and  intensity  or  extensity  of  sensation,  but  are  in- 
ferential processes,  founded  in  the  empirically  coordinated  conse- 
quences of  experience.  Innumerable  secondary  and  essentially 
unrelated  criteria  may  be  utilized  in  the  recognition  and  in  the 
judgment,  which  is  a  purely  qualitative  one,  not  "How  much  joint 
movement  or  skin  tension  is  now  felt  ? ' '  but  ' '  What  signs  can  I  find 
to  help  me  recognize  this  movement  among  the  many  other  move- 
ments with  which  I  am  somewhat  familiar?"  Titchener^  finds  that 
so  irrelevant  a  thing  anatomically  as  the  way  in  which  the  arm  fell 
down  against  the  side  after  completing  the  movement  was  in  one 
case  the  basis  for  the  judgment  of  extent  of  arm  movement.  Even 
in  judgments  of  resistance,  as  Bolton^"  has  pointed  out:  "Percep- 
tions of  greater  do  not  necessarily  rest  upon  greater  perceptions  and 
a  sensation  of  intensity  is  not  an  intense  sensation."  "Judgments 
of  same  and  heavier  are  inferences  from  certain  facts,  and  these 
facts  are  the  excitations  of  areas  in  the  one  case  that  remain  un- 
affected in  the  other. ' ' 

Woodworth  concludes  that  "there  must  be  a  sense  of  the  extent 
of  movement,  a  sense  which  is  not  reducible  to  a  sense  either  of  its 
force  or  of  its  duration  or  of  its  initial  and  terminal  positions.  "^^ 
There  is  no  contradiction  between  such  a  statement  and  the  one  just 
made.  To  say  that  we  have  a  direct  and  immediate  sense  of  the 
extent  of  movement  may  mean  just  what  is  here  suggested— that  a 
variety  of  qualitative  signs  have  been  learned  to  mean  movements 
of  definite  magnitudes,  irrespective  of  the  extensity  attribute  of  the 
particular  muscular,  tendinous,  articular  or  cutaneous  sensations 
involved.     Instead  of  insisting  on  the  prominence  of  any  one  of 

« "  Exper.  Psychol.,"  Vol.  2,  pt.  2,  2G0. 

"  Bolton  and  Withey,  "  On  the  Relation  of  Muscle  Sense  to  Pressure  Sense," 
Univ.  of  Nebraska  Studies,  1907,  7,  21. 

" "  Accuracy  of  Voluntary  Movement,"  Psychol.  Rev.,  Mon.  Supp.,  13,  80, 
1899. 


82  THE   INACCURACY    OF    MOVEMENT 

these  sources  it  seems  more  satisfactory  to  say  "wdth  Sherrington  that 
the  muscle  sense  is  based  on  a  "  specific  set  of  sensations  obtained  by 
specific  sense  organs  in  the  muscles,  joints  and  all  the  accessory 
organs  of  movement."^-  Any  sensitive  part  that  is  in  any  way 
uniformly  stimulated  in  the  process  of  a  given  movement  contributes 
its  share  to  the  character  of  the  movement  as  a  conscious  fact,  and 
any  such  contribution  may  be  utilized  in  the  recognition  of  the  move- 
ment when  it  occurs  again.  But  this  recognition  does  not  seem  to 
be  based  on  the  quantitative  relations  of  this  "specific  set  of  sensa- 
tions," nor  on  any  such  geometrical  correspondence  as  Kiilpe  sug- 
gests. It  is  throughout  a  qualitative  recognition.  Out  of  the  vari- 
ety of  stimulations  that  accompany  excursions  differing  in  direction, 
extent,  resistance  and  speed,  certain  combinations  have  been  learned 
to  mean  position,  others  distance,  others  resistance  or  strain  and  still 
others  velocity,  however  disproportionate  the  extensities  or  inten- 
sities of  the  sensations  in  their  own  right.  A  greater  intensity  of 
sensation  does  not  mean  a  greater  resistance  or  pressure.  It  may 
mean  a  lesser  objective  stimulus  under  more  sensitive  conditions. 
In  studying  the  accuracy  of  space  perception,  therefore,  and  in 
analyzing  any  tendency  to  error  found  there,  we  are  investigating 
just  this  association  of  sensation  complex  with  objective  meaning. 
From  this  fact  great  uncertainty  arises  in  the  application  of  the 
psychophysical  methods  to  the  study  of  movements.  Observers  tend 
here  to  refer  every  stimulus  to  some  absolute  scale  of  magnitudes 
and  to  estimate  and  compare,  not  by  a  genuine  balancing  of  impres- 
sion against  impression,  but  by  position  claimed  or  assigned  in  this 
absolute  or  practical  objective  scale.  Thus  two  movements  of  differ- 
ent extent  are  likely  to  be  felt,  not  so  much  as  "larger"  or  "smaller" 
impressions,  but  rather  as  impressions  that  are  qualitatively  differ- 
ent. Comparisons  are  seldom  made  in  subjective  terms.  Since  our 
movements  are  our  means  of  voluntarily  manipulating  our  environ- 
ment, they  come  to  be  specialized  for  specific  purposes  and  are  thus 
characterized  qualitatively  by  their  function.  A  movement  comes 
to  be  recognized  as  larger  than  another,  not  because  it  produces  a 
more  intense  sensation,  but  because  it  has  been  learned  to  he  a 
greater  movement — a  movement  that  will  effect  a  greater  change  in 
an  object  with  which  we  are  dealing.  The  element  of  extensity 
involved  in  movement  is  not  the  primary  quality  of  extensity  at- 
tributed to  all  or  most  of  our  other  sensations.  A  joint  or  tendon 
sensation  or  a  sensation  of  cutaneous  tension  may  possess  an  exten- 
sity of  its  own,  but  it  is  only  empirically  and  after  long  experience 
that  this  extensity  comes  to  mean  definite  extent  of  movement.  Or 
^  Stirling,  "  Outlines  of  Practical  Physiology,"  578.    London,  Griffen,  1902. 


CRITERIA    OF    TEE   JUDGMENT    OF   EXTENT  83 

an  object  or  movement  may  come  to  be  felt  as  greater  than  another 
by  virtue  of  the  fact  that  one  excites  a  local  sign  that  the  other  has 
not  affected.  And  this  local  sign,  once  awakened,  constitutes  not  a 
quantitative  but  a  qualitative  distinction.  There  is  no  more  reason 
for  supposing  that  the  estimation  of  movement  depends  on  a  highly 
developed  joint  sense  than  there  is  for  believing  that  it  depends 
solely  on  any  other. 


SUMMARY    OF    EXPERIMENTAL    RESULTS 

Chapter  I.    Methods 

Description  of  apparatus  desired  to  record  simultaneously  and 
graphically  the  extent,  force,  duration  and  velocity  of  rectilinear 
arm  movements. 

Chapter  II.     The  Illusion  of  Impact 

INIovements  terminating  in  impact  are  affected  in  perception 
and  reproduction  with  a  large  positive  constant  error,  the  magni- 
tude of  which  depends  on  (a)  the  force  of  impact  and  (&)  the  point 
in  the  intended  movement  at  which  the  impact  occurs.  The  greater 
the  force  of  impact  and  the  less  the  amount  of  the  intended  move- 
ment already  accomplished,  the  greater  the  illusion. 

Practise  without  knowledge  has  no  effect  on  the  constant  error. 
The  result  of  practise  with  knowledge  is  not  to  decrease  the  illusion 
so  much  as  to  produce  a  deliberate  shift  in  the  scale  of  extent  cri- 
teria, leading  to  a  corresponding  negative  constant  error  in  the 
judgment  of  free  movements. 

The  illusion  may  be  explained  on  the  basis  of  (a)  the  original 
intention,  (6)  irradiation  of  the  stimulus,  (c)  increase  of  the  sen- 
sory elements  of  the  movement  complex  through  fusion  of  the  shock 
of  impact. 

Chapter  III.     The  ' ' iNDiFFEREisrcE  Point" 

With  respect  to  the  experiments  on  extent  of  movement  reported 
in  this  chapter: 

1.  No  magnitude  evinces  any  considerable  constant  error  of  re- 
production when  estimated  out  of  relation  to  a  group  or  series  of 
which  it  is  a  member. 

2.  The  same  absolute  magnitude  may  be  under  one  circumstance 
an  indifference  point,  under  another  affected  with  a  positive  con- 
stant error  or  again  with  a  negative  one. 

3.  A  periodic  indifference  point  can  be  found  within  the  total 
series  (8)  hy  working  with  its  special  sections  (A,  B  and  C). 

4.  The  gradual  extension  of  the  series  limits  is  accompanied  by  a 
corresponding  shift  in  the  region  of  indifference. 

5.  The  phenomenon  of  the  indifference  point,  so  far  as  it  occurs 
in  our  spatial  judgments  and  in  our  temporal  judginents,  at  least 
so  far  as  they  are  a  function  of  extent  of  movement,  is  of  central 

84 


8UMMARY   OF  EXPERIMENTAL   RESULTS  85 

origin,  and  its  position  depends  on  the  range  or  limits  of  the  mag- 
nitudes used  in  a  given  experiment. 

6.  The  constant  errors  do  not  so  much  represent  transformations 
in  a  memory  image  of  the  stimulus  in  question  as  they  do  the  effect 
on  a  present  judgment  of  the  persistence  of  the  mental  set  involved 
in  the  directions  of  previous  judgments. 

7.  If  the  interval  between  the  separate  judgments  is  sufficient  the 
first  dispositions  are  soon  dissipated  and  are  no  longer  adequate  to 
affect  the  succeeding  performance. 

8.  In  the  presence  of  such  grouped  or  serial  magnitudes  we  tend 
to  form  our  judgments  around  the  mode  or  central  tendency  of  the 
series.  Toward  this  mean  each  judgment  tends  by  virtue  of  a 
mental  set  corresponding  to  the  upper  and  lower  limits  of  the  total 
range  of  magnitudes.  This  is  the  equivalent,  for  judgment,  of 
Leuba  's  ' '  law  of  sense  memory. ' ' 

Chapter  IV.    Relation  between  Extent  and  Duration 

The  four  methods  of  separate  accuracy  test,  confusion,  correla- 
tion and  correction  fail  to  justify  the  assumption  that  the  perception 
of  any  one  characteristic  of  a  movement  is  more  primitive  or  funda- 
mental than  that  of  any  other. 

Extent  and  duration  can  be  reproduced  with  about  equal  accu- 
racy, the  difference  being  slightly  in  favor  of  duration.  But  the 
incidental  durations  of  movements  intended  to  be  of  equal  extent 
show  a  variable  error  which  is  greater  than  that  of  their  correspond- 
ing extents  as  well  as  that  of  the  same  duration  magnitudes  when 
deliberately  reproduced. 

Constant  errors  seem  to  be  bound  up  with  the  process  of  deliberate 
reproduction,  the  constant  error  for  the  magnitude  attended  to 
(extent  or  time)  being  greater  than  that  of  the  magnitude  incident- 
ally reproduced  (time  or  extent).  Thus  the  constant  errors  for 
deliberate  extent  and  for  deliberate  time  are  both  greater  than  those 
for  incidental  extent  and  incidental  time. 

The  coefficients  of  correlation  show  that,  disregarding  the  magni- 
tude of  the  errors,  there  is  considerable  positive  correlation  between 
their  directions  for  extent  and  duration,  no  matter  which  factor  is 
being  attended  to. 

Subsequent  guesses  as  to  the  probable  direction  of  the  error  of 
attempts  to  reproduce  either  extent  or  duration  correspond  more 
closely  to  the  actual  relations  of  the  extents  than  to  those  of  the  dura- 
tions. The  proportion  of  right  guesses  in  reproduction  of  extent  is 
greater  than  in  reproduction  of  duration. 

These  facts  point  to  separate  processes  of  judgment  for  the  two 


86  THE  INACCURACY   OF   MOVEMENT 

magnitudes  (extent  and  duration).  There  is  at  least  no  justification 
for  the  attribution  of  more  fundamental  character  to  the  perception 
of  either.  The  judgment  of  extent  seems  to  be  based  on  a  system  of 
signs  which  have  been  learned  to  mean  extent  directly.  The  same 
seems  to  be  true  of  both  duration  and  velocity. 

Chapter  V,    ]\Iemory  for  Extent  and  Duration 

Within  the  limits  of  the  investigation  the  accuracy  of  reproduc- 
tion of  extents^  as  measured  by  the  variable  error,  is  not  influenced 
by  changes  in  the  time  interval.  "With  respect  to  the  constant  error 
individual  differences  are  shown. 

The  curve  of  memory  for  duration  follows  more  closely  the  ordi- 
nary statement  of  the  ' '  law  of  forgetting, ' '  in  the  case  of  the  constant 
error,  although  the  variable  error  undergoes  little  change  up  to  an 
interval  of  30  seconds. 

Chapter  VI.     The  Degree  op  Contraction 

The  Woodworth  modification  of  the  Loeb  illusion  is  present  in 
nearly  every  case  of  rectilinear  arm  movement.  The  middle  segments 
of  a  total  excursion  are  underestimated  in  comparison  with  the  seg- 
ments at  either  extreme. 

When  the  differences  in  position  between  adjacent  segments  is 
considerable,  the  total  swing  thus  consisting  of  but  few  segments 
(3-4),  the  durations  show  just  the  reverse  phenomenon— initial  and 
terminal  segments  frequently  tending  to  require  longer  time  than 
intermediate  segments.  When  the  differences  in  position  are  less 
(6  and  7  segments)  the  correlation  is  positive— extents  and  durations 
tend  to  vary  in  the  same  direction. 

The  average  deviation  for  the  durations  is  only  about  half  as 
great  as  that  for  the  extents,  but  this  is  not  necessarily  due  to  a  more 
fundamental  character  of  the  perception  of  time. 

There  is  a  tendency  in  reproduction  to  repeat  the  original  per- 
formance as  a  whole.  By  the  conditions  of  the  experiment  the  spa- 
tial judgment  is  confused  while  the  perception  of  duration  is  un- 
disturbed. 

Chapter  VII,     Criteria  op  the  Judgment  of  Extent 

Attempts  to  find  a  single  anatomical  or  topographical  source  for 
the  sensations  which  serve  as  criteria  of  extent  of  movement  are  con- 
tradictory and  futile.  Judgment  and  discrimination  are  inferential 
processes,  founded  in  the  empirically  coordinated  consequences  of  ex- 
perience.    Any  sensitive  part  that  is  in  any  way  uniformly  stimu- 


SUMMARY    OF   EXPERIMENTAL    RESULTS  87 

lated  in  the  process  of  a  given  movement  contributes  ite  share  to  the 
character  of  the  movement  as  a  conscious  fact,  and  any  such  contribu- 
tion may  be  utilized  in  the  recognition  of  the  movement  when  it 
occurs  again.  A  movement  comes  to  be  recognized  as  larger  than 
others,  not  because  it  produces  a  more  intense  sensation,  nor  because 
of  any  geometrical  correspondence  of  internal  and  external  points, 
but  because  it  has  been  learned  to  he  a  larger  movement— one  that 
will  effect  a  greater  change  in  an  object  with  which  we  are  dealing. 
Topographical  treatment  of  the  criteria  of  judgments  of  magnitude 
involves  an  "anatomist's  fallacy." 


{ 


AA    000  807129    2 
CENTRAL  UNIVERSITY  LIBRARY 
University  of  California,  San  Diego 


DATE  DUE 


J»!   2taaft^ 


MAR  1  9  1975 

MAR   T  ,f   ,qf^. 


C/39 


,^ 


[/CSD  Libr. 


